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()Tj
/F2 1 Tf
0.9169 0 TD
-0.0004 Tc
[(in)-334.7(\()]TJ
/F12 1 Tf
1.5556 0 TD
0 Tc
()Tj
/F6 1 Tf
1.7779 0 TD
(,)Tj
/F12 1 Tf
0.4436 0 TD
()Tj
/F2 1 Tf
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-0.0004 Tc
(2\).)Tj
-15.7442 -2.1844 TD
-0.0002 Tc
[(W)82.6(e)-340.8(call)-341.2(a)-341.2(S)-0.2(alem)-341.3(g)0.2(raph)]TJ
/F11 1 Tf
10.2064 0 TD
0 Tc
(trivial)Tj
/F2 1 Tf
2.9342 0 TD
-0.0003 Tc
[(if)-341.6(it)-341.3(is)-341.2(non)27.7(b)-0.3(ipartite)-343.6(and)]TJ
/F6 1 Tf
-14.3403 -1.3 TD
0 Tc
()Tj
/F12 1 Tf
1.0226 0 TD
()Tj
/F17 1 Tf
1.1048 0 TD
(Z)Tj
/F2 1 Tf
0.6667 0 TD
-0.0002 Tc
[(,)-455.1(o)0.2(r)-430.6(i)0.2(t)-430.7(i)0.2(s)-430.5(b)-0.2(ipartite)-432(and)]TJ
/F6 1 Tf
10.5045 0 TD
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 179.208 670.719 Tm
(2)Tj
/F12 1 Tf
9.9626 0 0 9.9626 188.046 667.11 Tm
()Tj
/F17 1 Tf
1.1057 0 TD
(Z)Tj
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0.6667 0 TD
-0.0003 Tc
[(.)-734.3(F)82.4(or)-430.7(a)-429.9(n)-0.3(on)27.7(trivial)]TJ
-16.5417 -1.2999 TD
-0.0001 Tc
[(Salem)-382.7(g)0.3(raph,)-395.3(its)-382.6(asso)-27.7(ciated)-384.1(S)-0.1(alem)-382.7(n)27.9(um)28.3(b)-28.1(e)-0.1(r)]TJ
/F6 1 Tf
19.1048 0 TD
0 Tc
()Tj
/F2 1 Tf
0.5502 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(G)Tj
/F2 1 Tf
0.7859 0 TD
[(\))-383.5(i)0.4(s)-382.5(t)0.4(hen)]TJ
-20.8294 -1.3 TD
-0.0002 Tc
[(the)-383.3(larger)-383.6(r)-0.6(o)-27.8(o)0.2(t)-382.8(o)0.2(f)]TJ
/F6 1 Tf
8.0374 0 TD
0 Tc
(z)Tj
/F2 1 Tf
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(+1)Tj
/F6 1 Tf
1.5321 0 TD
-0.0004 Tc
(/z)Tj
/F2 1 Tf
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/F6 1 Tf
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()Tj
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[(in)-383.3(the)-383.3(n)-0.2(on)27.8(bipartite)-385.1(case,)]TJ
-13.8055 -1.3 TD
[(and)-277.6(o)0.2(f)]TJ
/F12 1 Tf
2.9694 0.72 TD
0 Tc
()Tj
ET
0 0 0 1 K
0 J 0 j 0.405 w 10 M []0 d
1 i
78.795 635.633 m
83.871 635.633 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 78.795 628.257 Tm
(z)Tj
/F2 1 Tf
0.617 0 TD
0.1084 Tc
(+1)Tj
/F6 1 Tf
1.3858 0 TD
0 Tc
(/)Tj
/F12 1 Tf
0.4995 0.72 TD
()Tj
ET
112.041 635.633 m
117.117 635.633 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 112.041 628.257 Tm
(z)Tj
/F2 1 Tf
0.7868 0 TD
(=)Tj
/F6 1 Tf
1.0552 0 TD
()Tj
/F2 1 Tf
0.86 0 TD
-0.0002 Tc
[(in)-277.6(the)-276.7(b)-0.2(ipartite)-278.5(case.)-426.2(\()0.2(Prop)-28.2(osition)]TJ
-9.8423 -1.3009 TD
[(3.1)-325(sho)28.2(w)0.2(s)-324.8(t)0.2(hat)]TJ
/F6 1 Tf
6.6218 0 TD
0 Tc
()Tj
/F2 1 Tf
0.5502 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(G)Tj
/F2 1 Tf
0.7859 0 TD
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[(\))-324(i)0.3(s)-324.7(i)0.3(ndeed)-324.4(a)-324(S)-0.1(alem)-324(n)27.9(um)28.3(b)-28.1(e)-0.1(r.\))-442.3(W)82.7(e)-323.5(c)-0.1(all)]TJ
/F6 1 Tf
-8.3464 -1.3 TD
0 Tc
()Tj
/F2 1 Tf
0.5502 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(G)Tj
/F2 1 Tf
0.7859 0 TD
0.2959 Tc
(\)a)Tj
/F11 1 Tf
1.4806 0 TD
0 Tc
[(gr)51.3(aph)-322.7(Salem)-323.2(n)0.3(umb)51.7(e)0.2(r)]TJ
/F2 1 Tf
9.1188 0 TD
-0.0002 Tc
[(and)-295.6(denote)-296.5(b)27.8(y)]TJ
/F6 1 Tf
6.4411 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 233.676 600.8521 Tm
-0.0001 Tc
(graph)Tj
/F2 1 Tf
9.9626 0 0 9.9626 256.977 602.346 Tm
[(the)-295.5(s)-0.4(et)]TJ
-21.6882 -1.3 TD
-0.0002 Tc
[(of)-373.1(all)-372.9(graph)-373.3(S)-0.2(alem)-372.9(n)27.8(um)28.2(b)-28.2(e)-0.2(rs.)-561.7(\()0.2(F)82.5(o)0.2(r)-372.8(a)-372(trivial)-373.8(Salem)-373.8(g)0.2(raph)]TJ
/F6 1 Tf
T*
0 Tc
(G)Tj
/F2 1 Tf
0.7859 0 TD
(,)Tj
/F6 1 Tf
0.6116 0 TD
()Tj
/F2 1 Tf
0.5502 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(G)Tj
/F2 1 Tf
0.7859 0 TD
-0.0001 Tc
[(\))-333.9(i)0.3(s)-333.8(a)-333.9(recipro)-27.7(c)-0.1(al)-333.9(quadratic)-334.4(Pisot)-334.8(n)27.9(um)28.3(b)-28.1(e)-0.1(r.\))]TJ
-1.9224 -1.3 TD
[(Our)-333.8(rst)-333(result)-333(is)-333.8(the)-333.5(f)0.1(ollo)28.3(wing:)]TJ
/F3 1 Tf
-1.1997 -2.5999 TD
-0.0003 Tc
[(T)37.2(heor)11.1(em)-238.7(1.1.)]TJ
/F11 1 Tf
6.0771 0 TD
-0.0001 Tc
[(The)-295.3(s)-0.4(et)-295.7(of)-295.1(limit)-296.6(p)51.2(oints)-295.9(o)-0.3(f)]TJ
/F6 1 Tf
10.8957 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 215.82 536.097 Tm
-0.0001 Tc
(graph)Tj
/F11 1 Tf
9.9626 0 0 9.9626 239.112 537.591 Tm
[(is)-295.9(some)-295.3(set)]TJ
/F6 1 Tf
-19.895 -1.3 TD
0 Tc
(S)Tj
/F13 1 Tf
6.9738 0 0 6.9738 47.016 523.146 Tm
-0.0001 Tc
(graph)Tj
/F11 1 Tf
9.9626 0 0 9.9626 70.812 524.64 Tm
0.0001 Tc
[(of)-344.6(Pisot)-345.2(n)0.4(umb)51.8(e)0.3(rs.)-456.6(F)76.5(urthermor)51.4(e,)]TJ
/F6 1 Tf
14.1967 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 218.07 523.146 Tm
-0.0001 Tc
(graph)Tj
/F12 1 Tf
9.9626 0 0 9.9626 240.372 524.64 Tm
0 Tc
()Tj
/F6 1 Tf
0.8618 0 TD
(S)Tj
/F13 1 Tf
6.9738 0 0 6.9738 255.069 523.146 Tm
-0.0001 Tc
(graph)Tj
/F11 1 Tf
9.9626 0 0 9.9626 278.856 524.64 Tm
-0.0004 Tc
(is)Tj
-23.8843 -1.3 TD
0.0001 Tc
[(close)51.8(d)-0.1(.)]TJ
/F2 1 Tf
1.1997 -2.5999 TD
-0.0002 Tc
[(In)-357.1([McKee)-357.1(et)-356.6(al.)-516.5(99,)-363.8(Corollary)-358.6(9],)-363.8(a)-356.6(c)-0.2(onstruction)-358(w)28.2(a)0.2(s)]TJ
-1.1997 -1.3 TD
-0.0001 Tc
[(giv)28.1(en)-416.6(for)-416.1(certain)-416.6(subsets)]TJ
/F6 1 Tf
11.267 0 TD
0 Tc
(S)Tj
/F15 1 Tf
6.9738 0 0 6.9738 159.84 476.454 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 168.552 472.836 Tm
-0.0004 Tc
(of)Tj
/F6 1 Tf
1.2205 0 TD
0 Tc
(S)Tj
/F2 1 Tf
1.0859 0 TD
-0.0002 Tc
(and)Tj
/F6 1 Tf
2.0272 0 TD
0 Tc
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 218.934 476.454 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 227.646 472.836 Tm
-0.0004 Tc
(of)Tj
/F6 1 Tf
1.2205 0 TD
0 Tc
(T)Tj
/F2 1 Tf
0.7236 0 TD
[(,)-435.9(u)0(sing)-415.1(a)]TJ
-20.6882 -1.3 TD
-0.0001 Tc
[(restricted)-465.4(class)-465.7(o)0.3(f)-466(g)0.3(raphs)-465.7(\(star-lik)28.1(e)-467.2(t)0.3(rees\).)-839.8(W)82.7(e)-464.5(sho)28.3(w)28.3(e)-0.1(d)]TJ
T*
-0.0003 Tc
(that)Tj
/F6 1 Tf
2.225 0 TD
0 Tc
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 70.281 450.552 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 78.75 446.9341 Tm
-0.0004 Tc
[(had)-392.5(its)-392.8(limit)-392.9(p)-28.4(oin)27.6(ts)-393.7(in)]TJ
/F6 1 Tf
10.1902 0 TD
0 Tc
(S)Tj
/F15 1 Tf
6.9738 0 0 6.9738 186.957 450.552 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 195.435 446.9341 Tm
-0.0003 Tc
[(and)-392.4(t)0.1(hat)-391.9(\(lik)27.9(e)]TJ
/F6 1 Tf
6.508 0 TD
0 Tc
(S)Tj
/F2 1 Tf
0.6712 0 TD
(\))Tj
/F6 1 Tf
0.7796 0 TD
(S)Tj
/F15 1 Tf
6.9738 0 0 6.9738 281.412 450.552 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 40.905 433.983 Tm
-0.0002 Tc
[(w)28.2(a)0.2(s)-365.5(c)-0.2(losed)-364.3(in)]TJ
/F17 1 Tf
6.1313 0 TD
0 Tc
(R)Tj
/F2 1 Tf
0.7218 0 TD
-0.0002 Tc
[(.)-537.3(T)0.2(he)-365.2(main)-365.2(aim)-364.7(of)-365(this)-365.5(pap)-28.2(e)-0.2(r)-364.7(i)0.2(s)-364.6(t)0.2(o)-364.7(push)]TJ
-6.8531 -1.3 TD
[(these)-333.6(i)0.2(deas)-334.8(a)0.2(s)-333.9(f)0(ar)-334(as)-333.9(w)28.2(e)-334.5(can.)]TJ
1.1997 -1.3 TD
-0.0003 Tc
[(W)82.5(e)-359(call)-359.4(elemen)27.7(ts)-361.1(of)]TJ
/F6 1 Tf
8.8857 0 TD
0 Tc
(S)Tj
/F13 1 Tf
6.9738 0 0 6.9738 147.492 406.587 Tm
-0.0001 Tc
(graph)Tj
/F11 1 Tf
9.9626 0 0 9.9626 171.414 408.081 Tm
0 Tc
[(gr)51.3(aph)-381.4(Pisot)-380.6(n)0.3(umb)51.7(e)0.2(rs)]TJ
/F2 1 Tf
8.9788 0 TD
0.5217 Tc
[(.T)522.1(h)521.7(e)]TJ
-22.0786 -1.3 TD
0 Tc
[(pro)-27.6(o)0.4(f)-425.3(o)0.4(f)-424.4(T)0.4(heorem)-426(1.1)-425.1(rev)28.2(e)0(als)-425.8(a)-424.2(w)28.4(a)28.4(y)-426.2(to)-425.1(represen)28(t)-424.2(g)0.4(raph)]TJ
T*
[(Pisot)-457.6(n)28(um)28.4(b)-28(e)0(rs)-456.5(b)28(y)-456(bi-v)28.2(ertex)-456.9(c)0(oloured)-458(g)0.4(raphs,)-486.5(w)0.4(hic)28(h)-458(w)28.4(e)]TJ
T*
-0.0003 Tc
(call)Tj
/F11 1 Tf
1.833 0 TD
0.0001 Tc
[(Pisot)-357.9(g)0.3(r)51.4(aphs)]TJ
/F2 1 Tf
5.3688 0 TD
0 Tc
(.)Tj
-6.0021 -1.3 TD
-0.0001 Tc
[(Since)-395.8(Bo)28.3(yd)-394.9(has)-395.2(long)-396.3(c)-0.1(onjectured)-394.9(that)]TJ
/F6 1 Tf
17.0568 0 TD
0 Tc
(S)Tj
/F2 1 Tf
1.066 0 TD
-0.0003 Tc
[(is)-394.5(the)-396(s)-0.6(et)-394.6(of)]TJ
-19.3225 -1.3009 TD
[(limit)-269.2(p)-28.4(oin)27.6(ts)-269(of)]TJ
/F6 1 Tf
6.3345 0 TD
0 Tc
(T)Tj
/F2 1 Tf
0.7236 0 TD
-0.0001 Tc
[(,)-280.6(a)0.3(nd)-267.5(that)-268(therefore)]TJ
/F6 1 Tf
8.6698 0 TD
0 Tc
(S)Tj
/F12 1 Tf
0.7606 0 TD
()Tj
/F6 1 Tf
0.7561 0 TD
(T)Tj
/F2 1 Tf
0.991 0 TD
-0.0002 Tc
[(is)-267.9(closed)-267.6([Bo)28.2(y)0(d)]TJ
-18.2357 -1.3 TD
[(77],)-352.1(our)-346.6(r)-0.6(esult)-346.7(i)0.2(s)-347.4(a)-347.6(step)-347.1(in)-347.1(the)-347.1(d)-0.2(irection)-348(of)-347.8(a)-346.7(p)-0.2(ro)-27.8(of)-347.8(of)-346.9(his)]TJ
T*
-0.0001 Tc
[(conjecture.)-444.1(Ho)28.3(w)28.3(e)-0.1(v)28.1(e)-0.1(r,)-331.2(w)28.3(e)-330.8(can)-329.9(nd)-329(elemen)27.9(ts)-331.1(in)]TJ
/F6 1 Tf
20.0434 0 TD
0 Tc
(T)Tj
/F12 1 Tf
0.9368 0 TD
()Tj
/F6 1 Tf
0.9928 0 TD
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 265.635 315.9211 Tm
-0.0001 Tc
(graph)Tj
/F2 1 Tf
9.9626 0 0 9.9626 40.905 304.4641 Tm
-0.0002 Tc
[(\(see)-266.7(Section)-267.6(11\))-267.2(and)-266.7(e)-0.2(lemen)27.8(t)0.2(s)-267.9(i)0.2(n)]TJ
/F6 1 Tf
14.026 0 TD
0 Tc
(S)Tj
/F12 1 Tf
0.7588 0 TD
()Tj
/F6 1 Tf
0.8654 0 TD
(S)Tj
/F13 1 Tf
6.9738 0 0 6.9738 202.932 302.97 Tm
-0.0001 Tc
(graph)Tj
/F2 1 Tf
9.9626 0 0 9.9626 225.936 304.4641 Tm
[(\(see)-266.6(Corollary)]TJ
-18.5725 -1.3 TD
-0.0002 Tc
[(10.3\),)-335.8(so)-333.1(graphs)-333.9(do)-334(not)-334(t)0.2(ell)-334(t)0.2(he)-333.6(whole)-335.4(story)83.1(.)]TJ
1.1997 -1.3 TD
-0.0001 Tc
[(It)-501(is)-500.9(clearly)-502.2(desirable)-501.5(to)-501(describ)-28.1(e)-499.7(all)-501.9(Salem)-502(g)0.3(raphs.)]TJ
-1.1997 -1.3 TD
-0.0002 Tc
[(While)-405.8(w)28.2(e)-405.8(ha)28.2(v)28(e)-405.8(not)-405.4(b)-28.2(een)-404.9(able)-405.8(to)-405.4(do)-405.4(this)-406.1(completely)83.1(,)-425.3(w)28.2(e)]TJ
T*
-0.0001 Tc
[(are)-321.7(a)0.3(ble)-321.7(i)0.3(n)-321.7(P)0.2(rop)-28.1(o)0.3(sition)-322.6(3.2)-322.2(to)-322.2(restrict)-320.4(the)-321.7(c)-0.1(lass)-322(o)0.3(f)-321.5(g)0.3(raphs)]TJ
T*
-0.0002 Tc
[(that)-391.8(can)-391.4(b)-28.2(e)-390.5(S)-0.2(alem)-391.9(g)0.2(raphs.)-615.9(N)0(aturally)-393(enough,)-406.3(w)28.2(e)-391.4(call)-391.8(a)]TJ
T*
-0.0001 Tc
[(Salem)-357.4(g)0.3(raph)-357.9(that)-357.4(happ)-28.1(ens)-357.3(to)-357.4(b)-28.1(e)-356.1(a)-357.4(t)0.3(ree)-357(a)]TJ
/F11 1 Tf
18.3333 0 TD
[(Salem)-379.3(t)-0.3(r)51.2(e)51.6(e)]TJ
/F2 1 Tf
4.5567 0 TD
0.5163 Tc
[(.I)516.1(n)]TJ
-22.89 -1.3 TD
-0.0002 Tc
[(Section)-334.5(7)-334(w)28.2(e)-334.5(c)-0.2(ompletely)-335.2(describ)-28.2(e)-332.7(all)-334.9(Salem)-334(t)0.2(rees.)]TJ
1.1997 -1.3 TD
-0.0001 Tc
[(In)-245.8(Section)-246.7(9)-246.3(w)28.3(e)-245.8(s)-0.4(ho)28.3(w)-246.3(t)0.3(hat)-247.2(t)0.3(he)-245.8(smallest)-247.2(kno)28.3(w)0.3(n)-246.7(e)-0.1(lemen)27.9(t)0.3(s)]TJ
-1.1997 -1.3 TD
-0.0003 Tc
[(of)-334.3(the)]TJ
/F6 1 Tf
2.8619 0 TD
0 Tc
(k)Tj
/F2 1 Tf
0.552 0 TD
-0.0001 Tc
[(th)-334.4(deriv)28.1(ed)-333.5(set)-333.9(o)0.3(f)]TJ
/F6 1 Tf
7.4818 0 TD
0 Tc
(S)Tj
/F2 1 Tf
1.0037 0 TD
-0.0002 Tc
[(b)-28.2(e)-0.2(long)-334.9(t)0.2(o)-334(t)0.2(he)]TJ
/F6 1 Tf
6.1403 0 TD
0 Tc
(k)Tj
/F2 1 Tf
0.552 0 TD
-0.0001 Tc
[(th)-333.5(deriv)28.1(ed)-334.4(set)]TJ
-18.5917 -1.3 TD
-0.0004 Tc
(of)Tj
/F6 1 Tf
1.0651 0 TD
0 Tc
(S)Tj
/F13 1 Tf
6.9738 0 0 6.9738 57.627 173.4601 Tm
-0.0001 Tc
(graph)Tj
/F2 1 Tf
9.9626 0 0 9.9626 77.976 174.954 Tm
-0.0002 Tc
[(.)-419.8(I)-0.4(n)-258.6(Section)-261.3(10,)-274.4(w)28.2(e)-260.4(nd)-258.6(all)-260.8(graphs)-258.9(ha)28.2(ving)-260.8(Mahler)]TJ
-3.721 -1.3 TD
-0.0001 Tc
[(measure)-286.5(a)0.3(t)-286.9(most)]TJ
/F13 1 Tf
6.9738 0 0 6.9738 116.1 165.927 Tm
0 Tc
(1)Tj
ET
116.1 164.501 m
120.078 164.501 l
S
BT
6.9738 0 0 6.9738 116.1 158.5651 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 121.266 162.0031 Tm
-0.0004 Tc
[(\(1)-128.3(+)]TJ
/F12 1 Tf
1.9224 0.8275 TD
0 Tc
()Tj
ET
148.725 170.45 m
153.711 170.45 l
S
BT
/F2 1 Tf
9.9626 0 0 9.9626 148.725 162.0031 Tm
-0.0002 Tc
[(5\).)-428.9(F)-0.6(inally)83.1(,)-297(i)0.2(n)-287.5(Section)-287.5(11)-287(w)28.2(e)-286.6(list)]TJ
-10.8224 -1.3 TD
-0.0001 Tc
[(some)-334.4(small)-333.9(Salem)-334.8(n)27.9(um)28.3(b)-28.1(e)-0.1(rs)-332.9(coming)-334.8(f)0.1(rom)-333.9(g)0.3(raphs.)]TJ
/F3 1 Tf
0 -3.8159 TD
-0.0003 Tc
[(2.)-1201.1(LEMMAS)-279(O)-0.2(N)-278.4(G)-0.1(RAPH)-280.2(E)0.1(IGENV)55.1(A)0(LUES)]TJ
/F2 1 Tf
0 -1.8998 TD
-0.0001 Tc
[(F)82.6(o)0.3(r)-238.1(a)-238.2(graph)]TJ
/F6 1 Tf
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(G)Tj
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[(,)-258.1(r)-0.6(ecall)-238.3(that)-239.2(its)-239.9(eigen)27.8(v)55.1(alues)-239.9(are)-237.8(dened)-238.7(to)-239.2(b)-28.2(e)]TJ
-5.9642 -1.3 TD
[(those)-334.5(o)0.2(f)-334.2(its)-334.8(adjacency)-335.2(matrix)]TJ
/F6 1 Tf
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(A)Tj
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(=\()Tj
/F6 1 Tf
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(a)Tj
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6.9738 0 0 6.9738 200.484 77.664 Tm
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(ij)Tj
/F2 1 Tf
9.9626 0 0 9.9626 207.504 79.1581 Tm
-0.0001 Tc
[(\),)-334.8(where)]TJ
/F6 1 Tf
3.8927 0 TD
0 Tc
(a)Tj
/F14 1 Tf
6.9738 0 0 6.9738 251.55 77.664 Tm
-0.0002 Tc
(ij)Tj
/F2 1 Tf
9.9626 0 0 9.9626 261.342 79.1581 Tm
0.2792 Tc
[(=1)-54.6(i)279.6(f)]TJ
4.2739 63.8 TD
-0.0002 Tc
(the)Tj
/F6 1 Tf
1.6189 0 TD
0 Tc
(i)Tj
/F2 1 Tf
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[(th)-231.6(and)]TJ
/F6 1 Tf
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0 Tc
(j)Tj
/F2 1 Tf
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[(th)-231.5(v)28(e)-0.2(rtices)-230.9(are)-230.6(j)0(oined)-232.4(b)27.8(y)-230.4(an)-230.6(edge)-231.5(\(adjacen)27.8(t\),)]TJ
-5.4483 -1.3 TD
-0.0001 Tc
[(and)-290.1(0)-290.6(otherwise.)-431.5(Because)]TJ
/F6 1 Tf
11.3004 0 TD
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(A)Tj
/F2 1 Tf
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[(is)-290.5(symmetric,)-300.6(all)-291.6(eigen)27.8(v)55.1(alues)]TJ
-12.3402 -1.2999 TD
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(of)Tj
/F6 1 Tf
1.1383 0 TD
0 Tc
(G)Tj
/F2 1 Tf
1.1202 0 TD
-0.0002 Tc
[(are)-333.6(r)-0.6(eal.)]TJ
-1.0588 -1.3 TD
[(The)-534.1(f)0(ollo)28.2(wing)-535.5(f)0(acts)-534.4(are)-533.2(e)-0.2(ssen)27.8(tial)-533.7(ingredien)27.8(ts)-535.3(in)-533.2(our)]TJ
-1.1997 -1.3 TD
0.0001 Tc
[(pro)-27.5(o)0.5(fs.)]TJ
/F3 1 Tf
0 -2.5999 TD
-0.0001 Tc
[(Lemma)-335.7(2.1.)-515.3(\(Interlacing)-334.8(T)37.4(heor)11.3(em.\))]TJ
/F2 1 Tf
16.6557 0 TD
0 Tc
[([Go)-27.6(d)0(sil)-389.8(a)0.4(nd)-390.3(Ro)28.4(yle)]TJ
-16.6557 -1.2999 TD
-0.0003 Tc
[(00,)-475.9(Theorem)-447.1(9.1.1])]TJ
/F11 1 Tf
8.8866 0 TD
0.0002 Tc
[(If)-461(a)-461.6(g)0.4(r)51.5(aph)]TJ
/F6 1 Tf
4.9524 0 TD
0 Tc
(G)Tj
/F11 1 Tf
1.2485 0 TD
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[(has)-462.1(eigenvalues)]TJ
/F6 1 Tf
7.2361 0 TD
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()Tj
/F13 1 Tf
6.9738 0 0 6.9738 532.134 622.623 Tm
(1)Tj
/F18 1 Tf
9.9626 0 0 9.9626 541.251 624.1171 Tm
()Tj
/F6 1 Tf
-23.822 -1.3 TD
0.1658 Tc
(...)Tj
/F18 1 Tf
1.4445 0 TD
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()Tj
/F6 1 Tf
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()Tj
/F14 1 Tf
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(n)Tj
/F11 1 Tf
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[(,)-343.9(a)-0.3(nd)-339.1(a)-340(vertex)-339.3(o)-0.3(f)]TJ
/F6 1 Tf
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(G)Tj
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[(is)-340(delete)51.7(d)-339.9(t)-0.2(o)-339(p)-0.2(r)51.3(o)51.3(d)-0.2(uc)51.7(e)-340.4(a)-339(gr)51.3(aph)]TJ
/F6 1 Tf
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(H)Tj
/F11 1 Tf
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[(with)-259.6(eigenvalues)]TJ
/F6 1 Tf
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()Tj
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6.9738 0 0 6.9738 393.489 596.721 Tm
(1)Tj
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()Tj
/F6 1 Tf
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(...)Tj
/F18 1 Tf
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()Tj
/F6 1 Tf
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()Tj
/F14 1 Tf
6.9738 0 0 6.9738 442.152 596.721 Tm
(n)Tj
/F15 1 Tf
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()Tj
/F13 1 Tf
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(1)Tj
/F11 1 Tf
9.9626 0 0 9.9626 457.776 598.215 Tm
-0.0001 Tc
[(,)-279.7(then)-260(the)-260.1(eigenvalues)]TJ
-15.4432 -1.3 TD
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(G)Tj
/F11 1 Tf
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(and)Tj
/F6 1 Tf
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0 Tc
(H)Tj
/F11 1 Tf
1.2711 0 TD
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[(interlac)51.6(e.)-460.4(Namely,)]TJ
/F6 1 Tf
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0 Tc
()Tj
/F13 1 Tf
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(1)Tj
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()Tj
/F6 1 Tf
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()Tj
/F13 1 Tf
6.9738 0 0 6.9738 370.971 561.846 Tm
(1)Tj
/F18 1 Tf
9.9626 0 0 9.9626 378.207 563.34 Tm
()Tj
/F6 1 Tf
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()Tj
/F13 1 Tf
6.9738 0 0 6.9738 394.533 561.846 Tm
(2)Tj
/F18 1 Tf
9.9626 0 0 9.9626 401.769 563.34 Tm
()Tj
/F6 1 Tf
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()Tj
/F13 1 Tf
6.9738 0 0 6.9738 418.293 561.846 Tm
(2)Tj
/F18 1 Tf
9.9626 0 0 9.9626 425.529 563.34 Tm
()Tj
/F12 1 Tf
1.0552 0 TD
0.1658 Tc
()Tj
/F18 1 Tf
1.4445 0 TD
0 Tc
()Tj
/F6 1 Tf
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()Tj
/F14 1 Tf
6.9738 0 0 6.9738 466.947 561.846 Tm
(n)Tj
/F15 1 Tf
0.7059 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
(1)Tj
/F18 1 Tf
9.9626 0 0 9.9626 485.343 563.34 Tm
()Tj
/F6 1 Tf
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()Tj
/F14 1 Tf
6.9738 0 0 6.9738 501.669 561.846 Tm
(n)Tj
/F6 1 Tf
9.9626 0 0 9.9626 508.752 563.34 Tm
(.)Tj
/F2 1 Tf
-19.3602 -3.4997 TD
-0.0001 Tc
[(W)82.7(e)-335.3(denote)-336.2(the)-336.2(largest)-335.7(eigen)27.9(v)55.2(alue)-337.1(o)0.3(f)-335.9(a)-335.7(graph)]TJ
/F6 1 Tf
19.5005 0 TD
0 Tc
(G)Tj
/F2 1 Tf
0.7859 0 TD
-0.0003 Tc
[(,)-336.8(c)-0.3(alled)]TJ
-21.4861 -1.2999 TD
(its)Tj
/F11 1 Tf
1.3506 0 TD
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(index)Tj
/F2 1 Tf
2.3036 0 TD
0.2995 Tc
[(,b)327.5(y)]TJ
/F6 1 Tf
1.9224 0 TD
0 Tc
()Tj
/F2 1 Tf
0.5836 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(G)Tj
/F2 1 Tf
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-0.0002 Tc
[(\).)-431.6(W)82.6(e)-290.2(call)-290.6(a)-290.7(g)0.2(raph)-290.2(that)-291.6(has)-290.5(all)-290.6(its)-291.4(eigen-)]TJ
-7.3346 -1.3 TD
-0.0001 Tc
[(v)55.2(alues)-419.6(in)-420.2(the)-420.2(i)0.3(n)27.9(t)0.3(erv)55.2(a)0.3(l)-419.7([)]TJ
/F12 1 Tf
10.1017 0 TD
0 Tc
()Tj
/F2 1 Tf
0.7778 0 TD
(2)Tj
/F6 1 Tf
0.4996 0 TD
(,)Tj
/F2 1 Tf
0.4436 0 TD
0.1658 Tc
[(2])-256.5(a)]TJ
/F11 1 Tf
2.2856 0 TD
-0.0001 Tc
[(cyclotomic)-437.2(gr)51.2(aph)]TJ
/F2 1 Tf
7.4005 0 TD
-0.0003 Tc
[(.)-702.7(Con-)]TJ
-21.5087 -1.3 TD
-0.0001 Tc
[(nected)-325.3(graphs)-324.7(that)-325.8(ha)28.3(v)28.1(e)-326.2(index)-325.1(at)-324.9(most)-325.8(2)-324.9(ha)28.3(v)28.1(e)-325.3(b)-28.1(een)-324.4(clas-)]TJ
T*
-0.0002 Tc
[(sied,)-333.1(and)-334.5(i)0.2(n)-333.6(f)0(act)-334(all)-334.9(are)-333.6(c)-0.2(yclotomic.)]TJ
/F3 1 Tf
0 -2.5999 TD
[(Lemma)-705.3(2.2.)]TJ
/F2 1 Tf
7.162 0 TD
-0.0003 Tc
[([Smith)-761(70],)-867.1([Neumaier)-761.3(82],)-866.2(see)-759.2(also)]TJ
-7.162 -1.3 TD
[([Cv)27.9(etk)27.9(o)28.1(vi)28.1()]TJ
4.1068 0 TD
-0.0002 Tc
[(c)-522.4(a)0.2(nd)-517.9(Ro)28.2(wlinson)-520.6(90,)-564.4(Theorem)-518.3(2.1])]TJ
/F11 1 Tf
16.4389 0 TD
0 Tc
[(The)-527.4(c)51.7(on-)]TJ
-20.5457 -1.3 TD
[(ne)51.7(cte)51.7(d)-461.8(cyclotomic)-460.5(gr)51.3(aphs)-460.2(ar)51.3(e)-460.5(p)-0.2(r)51.3(e)51.7(cisely)-461.2(the)-460.5(induc)51.7(e)51.7(d)-461.8(sub-)]TJ
0 -1.3009 TD
0.0001 Tc
[(gr)51.4(aphs)-447.4(of)-446.7(the)-447.8(gr)51.4(aphs)]TJ
/F2 1 Tf
9.6878 0.2529 TD
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 405.486 410.412 Tm
(6)Tj
/F6 1 Tf
9.9626 0 0 9.9626 409.959 411.906 Tm
(,)Tj
/F2 1 Tf
0.9567 0.2529 TD
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 424.539 410.412 Tm
(7)Tj
/F11 1 Tf
9.9626 0 0 9.9626 429.012 411.906 Tm
0.4702 Tc
[(,a)470(n)470.5(d)]TJ
/F2 1 Tf
3.0399 0.2529 TD
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 464.346 410.412 Tm
(8)Tj
/F11 1 Tf
9.9626 0 0 9.9626 468.819 411.906 Tm
0.0001 Tc
[(,)-470.1(a)-0.1(nd)-447.3(those)-446.9(o)-0.1(f)-446.7(the)]TJ
/F2 1 Tf
-16.5516 -1.3 TD
0 Tc
(\()Tj
/F6 1 Tf
0.3885 0 TD
(n)Tj
/F2 1 Tf
0.9025 0 TD
0.3018 Tc
[(+1)302.2(\))]TJ
/F11 1 Tf
1.9676 0 TD
0.0001 Tc
[(-vertex)-468.3(g)0.3(r)51.4(aphs)]TJ
/F2 1 Tf
6.927 0.2529 TD
0 Tc
()Tj
/F6 1 Tf
-0.2638 -0.2529 TD
(A)Tj
/F14 1 Tf
6.9738 0 0 6.9738 410.238 397.461 Tm
(n)Tj
/F2 1 Tf
9.9626 0 0 9.9626 420.318 398.955 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
(n)Tj
/F18 1 Tf
1.0777 0 TD
()Tj
/F2 1 Tf
1.2539 0 TD
-0.0004 Tc
(2\))Tj
/F11 1 Tf
0.888 0 TD
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(,)Tj
/F2 1 Tf
1.0361 0.2529 TD
()Tj
/F6 1 Tf
-0.234 -0.2529 TD
(D)Tj
/F14 1 Tf
6.9738 0 0 6.9738 472.5 397.461 Tm
(n)Tj
/F2 1 Tf
9.9626 0 0 9.9626 482.589 398.955 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
(n)Tj
/F18 1 Tf
1.0768 0 TD
()Tj
/F2 1 Tf
1.2539 0 TD
-0.0004 Tc
(4\))Tj
/F11 1 Tf
0.888 0 TD
0.4955 Tc
[(,a)495.3(s)28.1(i)495.9(n)]TJ
-21.541 -1.3 TD
0 Tc
[(Figur)51.3(e)-358.5(1.)]TJ
/F2 1 Tf
1.1997 -2.5999 TD
-0.0002 Tc
[(Clearly)83.1(,)-504.7(g)0.2(eneral)-470.4(cyclotomic)-471.8(graphs)-470.3(are)-470(g)0.2(raphs)-469.4(all)-470.4(of)]TJ
-1.1997 -1.3 TD
[(whose)-333.6(c)-0.2(onnected)-334.5(comp)-28.2(onen)27.8(ts)-335.7(are)-333.6(c)-0.2(yclotomic.)]TJ
1.1997 -1.3 TD
(An)Tj
/F11 1 Tf
1.7417 0 TD
0 Tc
[(internal)-453.6(p)51.3(ath)]TJ
/F2 1 Tf
6.115 0 TD
-0.0001 Tc
[(of)-437.1(a)-436(g)0.3(raph)]TJ
/F6 1 Tf
5.1177 0 TD
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(G)Tj
/F2 1 Tf
1.2223 0 TD
-0.0001 Tc
[(is)-436.8(a)-436.9(s)-0.4(equence)-435.6(of)-437.1(v)28.1(e)-0.1(r-)]TJ
-15.3964 -1.3 TD
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(tices)Tj
/F6 1 Tf
2.3551 0 TD
0 Tc
(x)Tj
/F13 1 Tf
6.9738 0 0 6.9738 333.081 319.755 Tm
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 337.545 321.249 Tm
0.1664 Tc
(,...,x)Tj
/F14 1 Tf
6.9738 0 0 6.9738 365.373 319.755 Tm
0 Tc
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 374.328 321.249 Tm
-0.0004 Tc
(of)Tj
/F6 1 Tf
1.2105 0 TD
0 Tc
(G)Tj
/F2 1 Tf
1.1916 0 TD
-0.0001 Tc
[(suc)27.9(h)-405.7(that)-406.2(all)-407.1(v)28.1(e)-0.1(rtices)-406.1(\(except)-406.2(p)-28.1(o)0.3(s-)]TJ
-9.4692 -1.3 TD
(sibly)Tj
/F6 1 Tf
2.4265 0 TD
0 Tc
(x)Tj
/F13 1 Tf
6.9738 0 0 6.9738 333.792 306.804 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 342.171 308.298 Tm
-0.0002 Tc
(and)Tj
/F6 1 Tf
2.0046 0 TD
0 Tc
(x)Tj
/F14 1 Tf
6.9738 0 0 6.9738 367.839 306.804 Tm
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 372.735 308.298 Tm
-0.0001 Tc
[(\))-393.5(a)0.3(re)-393.1(distinct,)]TJ
/F6 1 Tf
6.4809 0 TD
0 Tc
(x)Tj
/F14 1 Tf
6.9738 0 0 6.9738 442.998 306.804 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 450.225 308.298 Tm
-0.0002 Tc
[(is)-393.5(adjacen)27.8(t)-394.5(t)0.2(o)]TJ
/F6 1 Tf
6.4077 0 TD
0 Tc
(x)Tj
/F14 1 Tf
6.9738 0 0 6.9738 519.759 306.804 Tm
(i)Tj
/F13 1 Tf
0.404 0 TD
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(+1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 537.075 308.298 Tm
-0.0003 Tc
(for)Tj
/F6 1 Tf
-23.4028 -1.3 TD
0 Tc
(i)Tj
/F2 1 Tf
0.6513 0 TD
0.3072 Tc
(=1)Tj
/F6 1 Tf
1.5845 0 TD
0.1666 Tc
(,...,k)Tj
/F12 1 Tf
3.0092 0 TD
0 Tc
()Tj
/F2 1 Tf
1.0118 0 TD
-0.0004 Tc
(1,)Tj
/F6 1 Tf
1.1328 0 TD
0 Tc
(x)Tj
/F13 1 Tf
6.9738 0 0 6.9738 383.238 293.853 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 391.203 295.347 Tm
-0.0002 Tc
(and)Tj
/F6 1 Tf
1.9622 0 TD
0 Tc
(x)Tj
/F14 1 Tf
6.9738 0 0 6.9738 416.448 293.853 Tm
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 424.845 295.347 Tm
-0.0001 Tc
[(ha)28.3(v)28.1(e)-352.4(degree)-350.6(a)0.3(t)-352(l)0.3(east)-351.1(3,)-356.5(while)]TJ
/F6 1 Tf
-12.1377 -1.3 TD
0 Tc
(x)Tj
/F13 1 Tf
6.9738 0 0 6.9738 309.618 280.902 Tm
(2)Tj
/F6 1 Tf
9.9626 0 0 9.9626 314.082 282.3961 Tm
0.1664 Tc
(,...,x)Tj
/F14 1 Tf
6.9738 0 0 6.9738 341.91 280.902 Tm
0 Tc
(k)Tj
/F15 1 Tf
0.6324 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 360.675 282.3961 Tm
[(ha)28.4(v)28.2(e)-369.5(degree)-366.8(2)0.4(.)-547.9(A)0.2(n)]TJ
/F11 1 Tf
8.4873 0 TD
-0.0001 Tc
[(internal)-389.6(e)51.6(d)-0.3(ge)]TJ
/F2 1 Tf
6.0084 0 TD
-0.0003 Tc
[(is)-368.3(an)-368.9(edge)]TJ
-20.1924 -1.3 TD
[(on)-333.7(an)-334.6(in)27.7(ternal)-334.1(path.)]TJ
/F3 1 Tf
0 -2.5999 TD
-0.0002 Tc
[(Lemma)-278.9(2.3.)]TJ
/F11 1 Tf
0.3758 -2.0199 TD
0.0001 Tc
[(\(i\))-499.8(S)0.4(upp)51.4(o)-0.1(se)-545.4(that)-545.8(the)-545.4(c)51.8(o)-0.1(nne)51.8(cte)51.8(d)-548.5(gr)51.4(aph)]TJ
/F6 1 Tf
17.3242 0 TD
0 Tc
(G)Tj
/F11 1 Tf
1.3325 0 TD
0.0002 Tc
(has)Tj
/F6 1 Tf
1.9775 0 TD
0 Tc
(G)Tj
/F15 1 Tf
6.9738 0 0 6.9738 521.064 227.0281 Tm
()Tj
/F11 1 Tf
9.9626 0 0 9.9626 529.299 223.419 Tm
0.0002 Tc
[(as)-545.8(a)]TJ
-20.6222 -1.3 TD
0.0001 Tc
[(pr)51.4(op)51.4(er)-357.9(sub)51.8(g)0.3(r)51.4(aph.)-459.3(Then)]TJ
/F6 1 Tf
10.1839 0 TD
0 Tc
()Tj
/F2 1 Tf
0.5836 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(G)Tj
/F15 1 Tf
6.9738 0 0 6.9738 442.818 214.077 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 445.617 210.468 Tm
(\))Tj
/F6 1 Tf
0.6667 0 TD
0.2774 Tc
(<)Tj
/F2 1 Tf
1.6387 0 TD
0 Tc
(\()Tj
/F6 1 Tf
0.3885 0 TD
(G)Tj
/F2 1 Tf
0.7859 0 TD
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381.687 695.13 382.695 694.122 382.695 692.88 c
b*
411.944 692.889 m
429.944 692.889 l
B*
429.945 692.88 m
429.945 691.638 428.937 690.63 427.695 690.63 c
426.453 690.63 425.445 691.638 425.445 692.88 c
425.445 694.122 426.453 695.13 427.695 695.13 c
428.937 695.13 429.945 694.122 429.945 692.88 c
b*
414.195 692.88 m
414.195 691.638 413.187 690.63 411.945 690.63 c
410.703 690.63 409.695 691.638 409.695 692.88 c
409.695 694.122 410.703 695.13 411.945 695.13 c
413.187 695.13 414.195 694.122 414.195 692.88 c
b*
396.194 692.889 m
414.194 692.889 l
B*
414.195 692.88 m
414.195 691.638 413.187 690.63 411.945 690.63 c
410.703 690.63 409.695 691.638 409.695 692.88 c
409.695 694.122 410.703 695.13 411.945 695.13 c
413.187 695.13 414.195 694.122 414.195 692.88 c
b*
398.445 692.88 m
398.445 691.638 397.437 690.63 396.195 690.63 c
394.953 690.63 393.945 691.638 393.945 692.88 c
393.945 694.122 394.953 695.13 396.195 695.13 c
397.437 695.13 398.445 694.122 398.445 692.88 c
b*
474.944 692.889 m
492.944 692.889 l
B*
492.945 692.88 m
492.945 691.638 491.937 690.63 490.695 690.63 c
489.453 690.63 488.445 691.638 488.445 692.88 c
488.445 694.122 489.453 695.13 490.695 695.13 c
491.937 695.13 492.945 694.122 492.945 692.88 c
b*
477.195 692.88 m
477.195 691.638 476.187 690.63 474.945 690.63 c
473.703 690.63 472.695 691.638 472.695 692.88 c
472.695 694.122 473.703 695.13 474.945 695.13 c
476.187 695.13 477.195 694.122 477.195 692.88 c
b*
459.194 692.889 m
477.194 692.889 l
B*
477.195 692.88 m
477.195 691.638 476.187 690.63 474.945 690.63 c
473.703 690.63 472.695 691.638 472.695 692.88 c
472.695 694.122 473.703 695.13 474.945 695.13 c
476.187 695.13 477.195 694.122 477.195 692.88 c
b*
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461.445 691.638 460.437 690.63 459.195 690.63 c
457.953 690.63 456.945 691.638 456.945 692.88 c
456.945 694.122 457.953 695.13 459.195 695.13 c
460.437 695.13 461.445 694.122 461.445 692.88 c
b*
443.444 692.889 m
461.444 692.889 l
B*
461.445 692.88 m
461.445 691.638 460.437 690.63 459.195 690.63 c
457.953 690.63 456.945 691.638 456.945 692.88 c
456.945 694.122 457.953 695.13 459.195 695.13 c
460.437 695.13 461.445 694.122 461.445 692.88 c
b*
445.695 692.88 m
445.695 691.638 444.687 690.63 443.445 690.63 c
442.203 690.63 441.195 691.638 441.195 692.88 c
441.195 694.122 442.203 695.13 443.445 695.13 c
444.687 695.13 445.695 694.122 445.695 692.88 c
b*
EMC
BT
/F2 1 Tf
9.9626 0 0 9.9626 243.734 642.5161 Tm
0 0 0 1 k
()Tj
/F6 1 Tf
-0.2638 -0.2529 TD
(A)Tj
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(n)Tj
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(n)Tj
/F2 1 Tf
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()Tj
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(E)Tj
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(6)Tj
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()Tj
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(8)Tj
/F3 1 Tf
8.9664 0 0 8.9664 74.952 595.515 Tm
[(FIGURE)-282.9(1)]TJ
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9.9626 0 0 9.9626 113.8584 595.515 Tm
(.)Tj
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-0.0001 Tc
[(The)-347.9(m)0.2(aximal)-349(connected)-348.5(cyclotomic)-349.3(graphs)]TJ
19.798 0.2529 TD
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()Tj
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/F8 1 Tf
5.9776 0 0 5.9776 303.39 594.516 Tm
(6)Tj
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()Tj
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(8)Tj
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(n)Tj
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()Tj
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[(2\),)-348.9(a)0(nd)]TJ
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()Tj
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(n)Tj
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[(one)-342.7(m)0.4(ore)-341.7(t)0.3(han)-343.3(t)0.3(he)-341.7(subscript.)]TJ
/F2 1 Tf
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[(to)-354.9(get)]TJ
-22.0236 -1.3 TD
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[(ag)312.5(r)311.7(a)312.5(p)312.1(h)]TJ
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()Tj
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[(so)-333.1(that,)-334.9(b)27.8(y)-333.3(\(i\),)]TJ
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[(Lemma)-259(2.4.)]TJ
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[(\(See)-301([Cv)28(etk)28(o)28.2(vi)28.2()]TJ
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()Tj
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[(1)-493.1(\(the)]TJ
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T*
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ET
0 0 0 1 K
0.405 w
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S
BT
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ET
75.177 378.98 m
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S
BT
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()Tj
ET
106.803 378.98 m
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S
BT
/F6 1 Tf
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[(By)-333.4(Lemma)-335(2.3\(i\),)]TJ
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[(\),)-334.9(giving)-334.9(t)0.2(he)-334.5(result.)]TJ
ET
301.302 365.228 m
308.079 365.228 l
301.504 359.049 m
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307.885 359.049 m
307.885 365.034 l
301.302 358.856 m
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S
BT
/F3 1 Tf
9.9626 0 0 9.9626 63 322.131 Tm
-0.0003 Tc
[(3.)-1201.1(SALEM)-279.4(GRAPHS)]TJ
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[(be)-440(a)-439.5(g)28.4(r)27.6(a)28.4(p)28(h)-440(o)28.4(n)]TJ
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(G)Tj
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(\()Tj
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(x)Tj
/F2 1 Tf
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[(\))-467.9(b)-28.4(e)-468.4(its)]TJ
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[(c)27.8(h)-0.2(aracteristic)-382.4(p)-28.2(olynomial)-383.7(\(the)-381.4(c)27.8(haracteristic)-382.4(p)-28.2(olynomial)]TJ
T*
[(of)-334.2(the)-333.6(a)0.2(djacency)-334.2(matrix)-335.2(of)]TJ
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[(rec)-51.2(i)-51(p)-51.6(roca)-51.6(l)-388.5(po)-51.6(l)-51.5(y)-51(-)]TJ
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(nomial)Tj
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[(,)-333.9(denoted)]TJ
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(G)Tj
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(\()Tj
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(x)Tj
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[(\),)-334.2(b)27.6(y)]TJ
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(G)Tj
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(\()Tj
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(\)=)Tj
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(n)Tj
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()Tj
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/F6 1 Tf
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[(By)-410(construction,)]TJ
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(G)Tj
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[(is)-409.8(indeed)-410.4(a)-409(r)-0.6(ecipro)-27.8(c)-0.2(al)-409.9(p)-28.2(olynomial,)]TJ
-9.5902 -1.3 TD
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[(is)-333.8(dened)-333.5(b)27.9(y)]TJ
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(G)Tj
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()Tj
ET
203.112 123.605 m
208.188 123.605 l
S
BT
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9.9626 0 0 9.9626 203.112 115.743 Tm
(z)Tj
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ET
238.626 123.605 m
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S
BT
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(z)Tj
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[(In)-243.1(this)-244.3(case)]TJ
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(G)Tj
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(G)Tj
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[(\))-243.6(a)0.3(nd)-243.1(the)-244(c)27.9(haracteristic)]TJ
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26.4002 47.5537 TD
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[(sees)-413.3(that)]TJ
/F6 1 Tf
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(R)Tj
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(G)Tj
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(\()Tj
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(z)Tj
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[(\))-414.3(i)0.3(s)-415.1(i)0.3(ndeed)-414.8(a)-414.3(p)-28.1(olynomial,)-437.8(and)-413.9(t)0.3(he)-414.8(corre-)]TJ
-6.6687 -1.3 TD
[(sp)-28.1(ondence)-476.2(is)-476.5(b)-28.1(e)-0.1(t)28.3(w)28.3(een)-478(the)-477.1(p)-0.1(airs)]TJ
/F12 1 Tf
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0.0523 Tc
(,)Tj
/F12 1 Tf
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()Tj
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/F12 1 Tf
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(,)Tj
-24.3191 -1.3 TD
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/F6 1 Tf
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()Tj
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(=)Tj
/F12 1 Tf
1.0551 0.7209 TD
()Tj
ET
381.564 534.401 m
387.981 534.401 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 381.564 527.016 Tm
()Tj
/F2 1 Tf
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/F12 1 Tf
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()Tj
ET
414.387 534.401 m
420.804 534.401 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 414.387 527.016 Tm
()Tj
/F2 1 Tf
0.6432 0 TD
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[(.)-410.7(\()0.3(W)82.7(e)-232.3(ma)28.3(y)-233.9(s)-0.4(upp)-28.1(ose)-232.3(t)0.3(hat)-232.7(t)0.3(he)-233.2(branc)27.9(h)]TJ
-9.5135 -1.2999 TD
[(of)-333.2(the)-334.4(s)-0.4(quare)-333.5(r)-0.5(o)-27.7(o)0.3(t)-333(i)0.3(s)-334.7(c)27.9(hosen)-333.5(s)-0.4(uc)27.9(h)-333.5(t)0.3(hat)]TJ
/F6 1 Tf
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()Tj
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()Tj
/F2 1 Tf
1.0561 0 TD
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(0.\))Tj
-17.5302 -1.3 TD
[(As)-348.4(the)-348.1(r)-0.7(o)-27.9(ots)-349.3(of)]TJ
/F6 1 Tf
6.9335 0 TD
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()Tj
/F14 1 Tf
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(G)Tj
/F2 1 Tf
9.9626 0 0 9.9626 423.441 501.114 Tm
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[(are)-348(all)-348.5(real,)-352.1(in)-348.9(b)-28.2(oth)-348(the)-348.9(n)-0.2(on)27.8(bipar-)]TJ
-9.779 -1.3 TD
[(tite)-398.6(and)-397.7(b)-0.2(ipartite)-398.6(cases)-398(t)0.2(he)-397.7(ro)-27.8(ots)-397.1(of)]TJ
/F6 1 Tf
16.2465 0 TD
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(G)Tj
/F2 1 Tf
9.9626 0 0 9.9626 506.088 488.163 Tm
-0.0001 Tc
[(are)-397.6(e)-0.1(ither)-398(real,)]TJ
-18.0747 -1.3 TD
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[(or)-376.4(lie)-376.9(on)-376(the)-376(unit)-376.5(c)-0.2(ircle.)-572.5(If)]TJ
/F6 1 Tf
12.165 0 TD
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[(2)-375.4(t)0.4(hen)-376.7(the)-375.8(a)0.4(b)-28(o)28.4(v)28.2(e)-376.7(corre-)]TJ
-14.2581 -1.3 TD
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[(sp)-28.1(ondences)-379(are)-379.5(with)-380.4(the)-379.5(p)-0.1(air)]TJ
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13.1632 0 TD
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[(,)-393.7(b)-28.3(oth)-380.6(p)-28.3(o)0.1(sitiv)27.9(e;)-403.7(if)]TJ
/F6 1 Tf
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()Tj
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([)Tj
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()Tj
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(2)Tj
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[(2)-166(])-427.1(then)-424.8(they)-424.6(are)-423.9(with)-425.7(the)-424.8(p)-0.2(air)]TJ
/F12 1 Tf
14.1705 0 TD
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1.5746 0 TD
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()Tj
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-24.3218 -1.3 TD
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[(b)-28.3(oth)-333.7(of)-334.3(mo)-27.9(dulus)-334.9(1.)]TJ
/F3 1 Tf
0 -2.5999 TD
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[(Pr)17.6(oposition)-268.9(3)0.3(.1.)]TJ
/F11 1 Tf
7.2632 0 TD
[(F)76.3(o)-0.3(r)-342.7(a)-342.7(c)0.1(yclotomic)-344.1(gr)51.2(aph)]TJ
/F6 1 Tf
10.3555 0 TD
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(,)Tj
/F6 1 Tf
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(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 523.449 408.963 Tm
(G)Tj
/F11 1 Tf
9.9626 0 0 9.9626 533.565 410.457 Tm
-0.0003 Tc
[(is)-343(inde)51.4(e)51.4(d)]TJ
-20.8327 -1.3 TD
0 Tc
[(a)-432.9(c)0.2(yclotomic)-434.3(p)51.3(o)-0.2(lynomial.)-687(F)76.4(or)-432.9(a)-432.9(n)0.3(ontrivial)-433.7(Salem)-433.4(g)0.2(r)51.3(aph)]TJ
/F6 1 Tf
T*
(G)Tj
/F11 1 Tf
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(,)Tj
/F6 1 Tf
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()Tj
/F2 1 Tf
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(\()Tj
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(G)Tj
/F2 1 Tf
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(\))Tj
/F11 1 Tf
0.7471 0 TD
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[(is)-358.2(inde)51.6(e)51.6(d)-359.8(a)-358(S)0.2(alem)-357.6(numb)51.6(er.)]TJ
-3.9225 -2.5999 TD
-0.0513 Tc
[(P)-51.4(roo)-51.5(f)-50.9(:)]TJ
/F2 1 Tf
3.3443 0 TD
-0.0001 Tc
[(F)82.6(r)-0.5(om)-469.4(the)-469.9(a)0.3(b)-28.1(o)28.3(v)28.1(e)-470.8(discussion,)-504.6(f)0.1(or)]TJ
/F6 1 Tf
14.3909 0 TD
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(G)Tj
/F2 1 Tf
1.2557 0 TD
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[(a)-470.5(c)-0.3(yclotomic)]TJ
-18.9909 -1.3 TD
-0.0001 Tc
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/F6 1 Tf
3.3109 0 TD
0 Tc
(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 366.57 344.208 Tm
(G)Tj
/F2 1 Tf
9.9626 0 0 9.9626 378.162 345.702 Tm
-0.0002 Tc
[(has)-492(all)-492.1(its)-492.9(ro)-27.8(ots)-492(of)-491.4(mo)-27.8(dulus)-492.9(1)-491.2(a)0.2(nd)-492.6(so)-491.2(is)-491.1(a)]TJ
-5.2342 -1.3 TD
[(cyclotomic)-336.3(p)-28.2(olynomial,)-336.7(b)27.8(y)-333.3(Kronec)27.8(k)28(e)-0.2(rs)-333.9(T)0.2(heorem.)]TJ
1.1997 -1.3 TD
[(W)82.6(e)-365.2(no)28.2(w)-366.6(tak)28(e)]TJ
/F6 1 Tf
6.0689 0 TD
0 Tc
(G)Tj
/F2 1 Tf
1.1518 0 TD
-0.0002 Tc
[(to)-366.5(b)-28.2(e)-365.2(a)-365.6(n)-0.2(on)27.8(trivial)-368.3(Salem)-366.6(g)0.2(raph,)-374.7(with)]TJ
-8.4204 -1.3 TD
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(index)Tj
/F6 1 Tf
2.7725 0 TD
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()Tj
/F2 1 Tf
0.991 0 TD
(=)Tj
/F6 1 Tf
1.1852 0 TD
()Tj
/F2 1 Tf
0.5836 0 TD
(\()Tj
/F6 1 Tf
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(G)Tj
/F2 1 Tf
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[(\).)-679.1(W)82.6(e)-411.3(can)-411.3(c)-0.2(onstruct)-411.7(its)-412.5(recipro)-27.8(c)-0.2(al)-411.7(p)-28.2(oly-)]TJ
-6.7067 -1.3 TD
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3.6334 0 TD
0 Tc
(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 369.783 292.4041 Tm
(G)Tj
/F2 1 Tf
9.9626 0 0 9.9626 376.479 293.898 Tm
0.4115 Tc
[(,a)411.9(n)411.5(d)]TJ
/F6 1 Tf
2.6966 0 TD
0 Tc
()Tj
/F2 1 Tf
0.9323 0 TD
(=)Tj
/F6 1 Tf
1.1599 0 TD
()Tj
/F2 1 Tf
0.5502 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(G)Tj
/F2 1 Tf
0.7859 0 TD
[(\))-397.1(i)0.4(s)-396(a)-396.2(ro)-27.6(ot)-396.1(of)-396.4(this.)-632.8(M)-0.3(oreo)28.4(v)28.2(e)0(r,)]TJ
/F6 1 Tf
-11.5786 -1.3009 TD
()Tj
/F2 1 Tf
0.9738 0 TD
-0.0003 Tc
[(is)-391.8(the)-391.5(o)0.1(nly)-391.3(r)-0.7(o)-27.9(o)0.1(t)-391.9(o)0.1(f)]TJ
/F6 1 Tf
8.49 0 TD
0 Tc
(P)Tj
/F14 1 Tf
6.9738 0 0 6.9738 426.699 279.444 Tm
(G)Tj
/F2 1 Tf
9.9626 0 0 9.9626 437.283 280.938 Tm
-0.0002 Tc
[(that)-391.8(is)-391.7(greater)-391.8(t)0.2(han)-392.3(2)0.2(,)-405.4(s)-0.5(o)-390.9(t)0.2(hat)]TJ
-11.1684 -1.3 TD
-0.0001 Tc
[(apart)-380.9(f)0.1(rom)]TJ
/F6 1 Tf
5.1276 0 TD
0 Tc
()Tj
/F2 1 Tf
0.9639 0 TD
-0.0001 Tc
[(and)-380.4(p)-28.1(ossibly)]TJ
/F12 1 Tf
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()Tj
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()Tj
/F2 1 Tf
0.9639 0 TD
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[(all)-382.1(the)-380.7(r)-0.8(o)-28(ots)-382(of)]TJ
/F6 1 Tf
6.975 0 TD
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(P)Tj
/F14 1 Tf
6.9738 0 0 6.9738 538.551 266.493 Tm
(G)Tj
/F2 1 Tf
9.9626 0 0 9.9626 549.036 267.9871 Tm
-0.0004 Tc
[(lie)-381.6(in)]TJ
-22.3856 -1.3 TD
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[(the)-394.9(r)-0.5(eal)-394.4(i)0.3(n)27.9(t)0.3(erv)55.2(a)0.3(l)-395.3([)]TJ
/F12 1 Tf
7.7438 0 TD
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()Tj
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(2)Tj
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(,)Tj
/F2 1 Tf
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[(2)-166.1(])0.1(.)-630.4(A)-0.1(s)-394.5(n)-0.3(oted)-396(a)0.1(b)-28.3(o)28.1(v)27.9(e)-0.3(,)-410.9(s)-0.6(uc)27.7(h)-394.2(r)-0.7(o)-27.9(ots)-395.4(of)]TJ
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(M)Tj
/F2 1 Tf
9.9626 0 0 9.9626 271.044 325.2361 Tm
-0.0002 Tc
(can)Tj
-23.1002 -1.3 TD
[(b)-28.2(e)-313.7(one)-313.7(o)0.2(f)-314.4(1)0.2(8)-314.1(g)0.2(raphs,)-318.7(e)-0.2(ac)27.8(h)-313.7(with)-315.5(at)-314.1(most)-314.1(1)0.2(0)-314.1(v)28(ertices.)-438.8(N)0(ote)]TJ
T*
-0.0003 Tc
(that)Tj
/F6 1 Tf
2.0868 0 TD
0 Tc
(G)Tj
/F12 1 Tf
0.7859 0 TD
(|)Tj
/F14 1 Tf
6.9738 0 0 6.9738 72.288 297.84 Tm
(M)Tj
/F2 1 Tf
9.9626 0 0 9.9626 83.664 299.334 Tm
-0.0001 Tc
[(has)-253.4(o)0.3(nly)-253.7(o)0.3(ne)-254(eigen)27.9(v)55.2(alue)-254.9(g)0.3(reater)-254.4(t)0.3(han)-254(2)0.3(,)-269.8(a)0.3(s)-254.3(w)0.3(hen)]TJ
-4.2919 -1.3 TD
[(a)-263.5(v)28.1(ertex)-263.7(i)0.3(s)-263.3(r)-0.5(emo)28.3(v)28.1(ed)-264.8(from)]TJ
/F6 1 Tf
10.8578 0 TD
0 Tc
(G)Tj
/F12 1 Tf
0.7859 0 TD
(|)Tj
/F14 1 Tf
6.9738 0 0 6.9738 159.669 284.889 Tm
(M)Tj
/F2 1 Tf
9.9626 0 0 9.9626 171.135 286.383 Tm
-0.0001 Tc
[(the)-263.9(r)-0.5(esulting)-264.4(g)0.3(raph)-263(has,)-277.9(b)27.9(y)]TJ
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[(minimalit)28.2(y)83.1(,)-307.8(index)-296.3(at)-297(most)-297(2)0.2(.)-432.5(H)0(ence,)-304.2(b)27.8(y)-296.3(Lemma)-297(2.1,)]TJ
/F6 1 Tf
22.6488 0 TD
0 Tc
(G)Tj
/F12 1 Tf
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(|)Tj
/F14 1 Tf
6.9738 0 0 6.9738 277.137 271.938 Tm
(M)Tj
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[(cannot)-334(h)-0.2(a)28.2(v)28(e)-335.4(more)-333.6(t)0.2(han)-334.5(o)0.2(ne)-333.6(eigen)27.8(v)55.1(alue)-335.4(g)0.2(reater)-334.9(t)0.2(han)-334.5(2)0.2(.)]TJ
1.1997 -1.3 TD
-0.0001 Tc
[(No)28.3(w)-288.8(l)0.3(et)]TJ
/F6 1 Tf
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(A)Tj
/F2 1 Tf
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[(b)-28.2(e)-286.6(the)-288.4(s)-0.5(et)-287(of)-287.3(v)28(e)-0.2(rtices)-288.7(in)]TJ
/F6 1 Tf
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(V)Tj
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(G)Tj
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/F12 1 Tf
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()Tj
/F6 1 Tf
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(M)Tj
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[(adjacen)27.9(t)]TJ
-20.9332 -1.3 TD
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(in)Tj
/F6 1 Tf
1.1365 0 TD
0 Tc
(G)Tj
/F2 1 Tf
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-0.0001 Tc
[(to)-304.1(a)-303.2(v)28.1(ertex)-303.4(o)0.3(f)]TJ
/F6 1 Tf
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(M)Tj
/F2 1 Tf
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-0.0001 Tc
[(.)-434.2(T)0.3(hen,)-309.5(b)27.9(y)-303.4(in)27.9(terlacing,)-312.2(the)-303.7(i)0.3(nduced)]TJ
-9.4106 -1.3 TD
0 Tc
(subgraph)Tj
/F6 1 Tf
4.4555 0 TD
(G)Tj
/F15 1 Tf
6.9738 0 0 6.9738 93.123 225.237 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 100.377 221.6281 Tm
-0.0004 Tc
(on)Tj
/F6 1 Tf
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(V)Tj
/F2 1 Tf
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(\()Tj
/F6 1 Tf
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(G)Tj
/F2 1 Tf
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(\))Tj
/F12 1 Tf
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()Tj
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(A)Tj
/F2 1 Tf
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-0.0002 Tc
[(has)-447.7(a)0.2(t)-446.9(most)-447.8(o)0.2(ne)-447.4(eigen)27.8(v)55.1(alue)]TJ
-12.4124 -1.3009 TD
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[(greater)-350.1(t)0.3(han)-349.7(2)0.3(,)-353.8(w)0.3(hic)27.9(h)-350.6(m)28.3(u)-0.1(st)-349.3(b)-28.1(e)-348.8(the)-349.7(i)0.3(ndex)-349.5(of)]TJ
/F6 1 Tf
19.2403 0 TD
0 Tc
(G)Tj
/F12 1 Tf
0.7859 0 TD
(|)Tj
/F14 1 Tf
6.9738 0 0 6.9738 243.18 207.174 Tm
(M)Tj
/F2 1 Tf
9.9626 0 0 9.9626 252.027 208.6681 Tm
[(.)-491.9(H)0.2(ence)]TJ
-21.1914 -1.3 TD
-0.0002 Tc
[(the)-341.7(other)-342.1(comp)-28.2(onen)27.8(ts)-342.9(of)]TJ
/F6 1 Tf
11.0114 0 TD
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(G)Tj
/F15 1 Tf
6.9738 0 0 6.9738 158.436 199.3351 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 164.637 195.717 Tm
-0.0001 Tc
[(m)28.3(u)-0.1(st)-341.1(together)-342.9(form)-341.2(a)-341.2(c)-0.1(yclo-)]TJ
-12.4196 -1.3 TD
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[(tomic)-336.3(graph,)]TJ
/F6 1 Tf
5.8946 0 TD
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(H)Tj
/F2 1 Tf
1.2467 0 TD
[(sa)28.4(y)83.3(.)-448.5(By)-335(denition,)-336.5(t)0.4(here)-334.3(a)0.4(re)-335.2(no)-333.8(edges)-335.5(in)]TJ
/F6 1 Tf
-7.1413 -1.3 TD
(G)Tj
/F2 1 Tf
1.1193 0 TD
-0.0001 Tc
[(ha)28.3(ving)-334.8(one)-334.4(endv)28.1(ertex)-333.2(i)0.3(n)]TJ
/F6 1 Tf
10.809 0 TD
0 Tc
(M)Tj
/F2 1 Tf
1.412 0 TD
-0.0002 Tc
[(and)-334.5(t)0.2(he)-333.6(other)-334.9(in)]TJ
/F6 1 Tf
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(H)Tj
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(.)Tj
-20.5005 -1.3 TD
-0.0002 Tc
[(As)-239(the)-238.7(i)0.2(ndex)-238.5(of)]TJ
/F6 1 Tf
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[(,)-257.1(t)0.3(he)-238.6(maxim)28.3(um)-240(degree)-237.7(o)0.3(f)-239.3(a)-238.2(v)28.1(e)-0.1(rtex)]TJ
-10.3699 -1.3 TD
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(of)Tj
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(G)Tj
/F2 1 Tf
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-0.0001 Tc
[(is)-341(b)-28.1(o)0.3(unded)-339.8(b)27.9(y)]TJ
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6.498 0 TD
0 Tc
()Tj
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6.9738 0 0 6.9738 134.091 147.531 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 138.564 143.9131 Tm
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[(,)-342.2(b)27.7(y)-340.7(L)-0.4(emma)-340.4(2.4.)-466.9(Applying)-341.3(this)-341.2(to)]TJ
-9.8025 -1.3 TD
-0.0001 Tc
[(the)-444.6(v)28.1(ertices)-444(of)]TJ
/F6 1 Tf
6.8115 0 TD
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(M)Tj
/F2 1 Tf
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[(,)-471.2(w)28.3(e)-444.6(s)-0.4(ee)-443.7(that)-444.1(there)-443.7(a)0.3(re)-444.6(at)-444.1(most)-444.1(1)0.3(0)]TJ
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()Tj
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(2)Tj
/F2 1 Tf
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-0.0001 Tc
[(edges)-288.6(with)-289.2(one)-288.3(endv)28.1(ertex)-289(i)0.3(n)]TJ
/F6 1 Tf
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(M)Tj
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[(and)-288.4(t)0.2(he)-288.4(other)-289.7(in)]TJ
/F6 1 Tf
7.2659 0 TD
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(A)Tj
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[(.T)430(h)457.6(u)429.6(s)]TJ
-21.693 -1.3 TD
-0.0002 Tc
[(the)-438.4(s)-0.5(ize)-438.4(#)]TJ
/F6 1 Tf
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(A)Tj
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(of)Tj
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(A)Tj
/F2 1 Tf
1.1879 0 TD
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[(is)-437.9(at)-438.9(most)-438.9(1)0.1(0)]TJ
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()Tj
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(2)Tj
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-0.0002 Tc
[(.)-758.6(N)0(o)28.2(w)0.2(,)-465(a)0.2(pplying)-439.7(the)]TJ
-15.3014 -1.3 TD
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[(degree)-438.2(b)-28(ound)]TJ
/F6 1 Tf
6.4077 0 TD
()Tj
/F13 1 Tf
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(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 119.385 92.109 Tm
-0.0002 Tc
[(to)-438.8(the)-439.3(v)28(ertices)-439.6(of)]TJ
/F6 1 Tf
8.1232 0 TD
0 Tc
(A)Tj
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[(,)-465.1(w)28.1(e)-439.4(s)-0.6(imilarly)-440(get)]TJ
-16.7505 -1.3 TD
0 Tc
[(the)-481.5(upp)-28(er)-481(b)-28(o)0.4(und)]TJ
/F6 1 Tf
8.1133 0 TD
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 127.548 82.776 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 132.021 79.1581 Tm
(#)Tj
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(A)Tj
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[(for)-482.1(t)0.2(he)-481.7(n)27.8(u)-0.2(m)28.2(b)-28.2(er)-482.1(of)-482.4(edges)-482(with)]TJ
15.1902 63.8 TD
0 Tc
[(one)-327.9(endv)28.2(ertex)-328.6(i)0.4(n)]TJ
/F6 1 Tf
7.5704 0 TD
(A)Tj
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[(and)-329.1(t)0.2(he)-329.1(other)-328.5(in)]TJ
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(H)Tj
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[(.)-443.1(T)0.4(hese)-327.9(edges)-328.3(are)]TJ
-16.9872 -1.3 TD
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[(a)275.5(d)275.1(j)275.3(a)275.5(c)275.1(e)275.1(n)303.1(tt)275.5(oa)275.5(tm)275.5(o)275.5(s)274.8(t)]TJ
/F6 1 Tf
8.6589 0 TD
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()Tj
/F13 1 Tf
6.9738 0 0 6.9738 396 705.441 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 400.464 701.823 Tm
(#)Tj
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(A)Tj
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[(v)28(e)-0.2(rtices)-275.2(in)]TJ
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(H)Tj
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[(of)-275.4(degree)-273.8(g)0.3(reater)]TJ
-17.4036 -1.2999 TD
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[(than)-309.3(2)-308.8(i)0.1(n)]TJ
/F6 1 Tf
4.2586 0 TD
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(G)Tj
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[(.)-436.1(E)0.1(v)28(e)-0.2(ry)-309(connected)-309.2(cyclotomic)-311(graph)-309.2(c)-0.2(on)27.8(tains)]TJ
-5.0445 -1.3 TD
[(at)-262.7(most)-262.7(t)28.2(w)28.2(o)-263.6(v)28(e)-0.2(rtices)-263.4(of)-262.9(degree)-262.2(g)0.2(reater)-263.5(t)0.2(han)-263.1(2)-261.8(\(in)-263.1(fact)-263.6(only)]TJ
T*
[(the)-447.4(t)28.2(yp)-28.2(e)]TJ
4.432 0.2529 TD
0 Tc
()Tj
/F6 1 Tf
-0.2331 -0.2529 TD
(D)Tj
/F14 1 Tf
6.9738 0 0 6.9738 353.997 661.4761 Tm
(n)Tj
/F2 1 Tf
9.9626 0 0 9.9626 359.424 662.97 Tm
-0.0002 Tc
[(,)-474.9(a)0.2(s)-446.8(i)0.2(n)-447.4(F)-0.6(igure)-447.4(1,)-474.9(ha)28.2(ving)-448.8(t)28.2(w)28.2(o\).)-786.6(Also,)-475.8(s)-0.5(ince)]TJ
-5.5711 -1.3 TD
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[(ev)28.1(ery)-410.9(c)-0.1(onnected)-411.2(comp)-28.1(onen)27.9(t)-411.6(o)0.3(f)]TJ
/F6 1 Tf
13.8679 0 TD
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(H)Tj
/F2 1 Tf
1.3226 0 TD
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[(has)-411.5(a)0.3(t)-411.6(l)0.3(east)-410.7(one)-411.2(s)-0.4(uc)27.9(h)]TJ
-15.1904 -1.3 TD
-0.0002 Tc
[(edge)-324.5(i)0.2(nciden)27.8(t)-325.9(i)0.2(n)-325.4(it,)-327.7(the)-324.5(n)27.8(um)28.2(b)-28.2(e)-0.2(r)-325.8(o)0.2(f)-325.2(s)-0.5(uc)27.8(h)-324.5(c)-0.2(omp)-28.2(onen)27.8(ts)-326.7(is)-324.8(at)]TJ
T*
(most)Tj
/F6 1 Tf
2.45 0 TD
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 334.143 627.726 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 338.607 624.1171 Tm
(#)Tj
/F6 1 Tf
0.8329 0 TD
(A)Tj
/F2 1 Tf
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[(.)-446.9(T)0.2(his)-333.9(giv)28(es)-335.7(at)-334(most)-334(a)0.2(nother)-335.8(2)]TJ
/F6 1 Tf
13.3005 0 TD
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()Tj
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6.9738 0 0 6.9738 492.696 627.726 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 497.16 624.1171 Tm
(#)Tj
/F6 1 Tf
0.8329 0 TD
(A)Tj
/F2 1 Tf
1.0841 0 TD
-0.0001 Tc
[(v)28.1(e)-0.1(rtices)]TJ
-21.3133 -1.3 TD
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[(of)-336.9(degree)-336.3(g)0.2(reater)-337.6(t)0.2(han)-338.1(2)-336.7(in)]TJ
/F6 1 Tf
11.9997 0 TD
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(H)Tj
/F2 1 Tf
1.2485 0 TD
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[(that)-337.6(are)-336.3(n)-0.2(ot)-337.6(adjacen)27.8(t)-337.6(t)0.2(o)-337.6(a)]TJ
-13.2481 -1.3 TD
-0.0282 Tc
[(ve)-28.2(r)-28.6(t)-27.8(e)-28.2(x)-351.4(o)-27.8(f)]TJ
/F6 1 Tf
4.1483 0 TD
0 Tc
(A)Tj
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[(.)-441.4(A)0.1(dding)-324(up,)-324.9(w)28.3(e)-323.5(see)-322.6(t)0.3(hat)-324(t)0.3(he)-323.5(total)-324.9(n)27.9(u)-0.1(m)28.3(b)-28.1(er)-323(of)]TJ
-4.8982 -1.3 TD
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[(v)28(e)-0.2(rtices)-318.5(of)-318.9(degree)-318.2(g)0.2(reater)-319.5(t)0.2(han)-319.1(2)-317.8(is)-319.4(at)-318.7(most)-318.7(#)]TJ
/F6 1 Tf
19.8067 0 TD
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(M)Tj
/F2 1 Tf
1.2711 0 TD
0.1916 Tc
(+#)Tj
/F6 1 Tf
1.8023 0 TD
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(A)Tj
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0.9422 0 TD
(+)Tj
/F6 1 Tf
-23.8223 -1.3 TD
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 309.735 575.922 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 314.199 572.313 Tm
(#)Tj
/F6 1 Tf
0.8329 0 TD
(A)Tj
/F2 1 Tf
1.3063 0 TD
0.2223 Tc
(+2)Tj
/F6 1 Tf
1.4996 0 TD
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 356.265 575.922 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 360.738 572.313 Tm
(#)Tj
/F6 1 Tf
0.8329 0 TD
(A)Tj
/F18 1 Tf
1.3614 0 TD
()Tj
/F2 1 Tf
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-0.0004 Tc
(10\(3)Tj
/F6 1 Tf
1.8872 0 TD
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 417.726 575.922 Tm
(4)Tj
/F2 1 Tf
9.9626 0 0 9.9626 424.422 572.313 Tm
(+)Tj
/F6 1 Tf
1 0 TD
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 440.199 575.922 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 446.886 572.313 Tm
-0.0004 Tc
[(+)-222.7(1\).)]TJ
-13.1504 -1.3009 TD
0 Tc
[(T)83.5(o)-398(b)-28(o)0.4(und)-397.5(the)-398.4(n)28(um)28.4(b)-28(e)0(r)-397.9(o)0.4(f)-398.2(v)28.2(ertices)-397.8(of)-398.2(degree)-397.5(1)0.4(,)-414.2(w)28.4(e)-398.4(a)0.4(s-)]TJ
-1.1997 -1.3 TD
-0.0001 Tc
[(so)-27.7(ciate)-422.9(to)-421.6(eac)27.9(h)-422.9(suc)27.9(h)-421.1(v)28.1(e)-0.1(rtex)-422.7(the)-422(nearest)-421.5(\(in)-422(the)-422(o)0.3(b)27.9(v)0.1(ious)]TJ
T*
0 Tc
[(sense\))-350.1(v)28.2(e)0(rtex)-352.1(of)-351.2(degree)-351.4(g)0.4(reater)-351.8(t)0.4(han)-352.3(2)0.4(,)-356.4(a)0.4(nd)-351.4(then)-351.4(use)-351.4(t)0.4(he)]TJ
T*
-0.0001 Tc
[(fact)-288.7(that)-288.7(these)-287.4(latter)-289.6(v)28.1(ertices)-288.6(ha)28.3(v)28.1(e)-289.2(degree)-288.3(a)0.3(t)-287.8(most)]TJ
/F6 1 Tf
21.7264 0 TD
0 Tc
()Tj
/F2 1 Tf
0.5836 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(G)Tj
/F2 1 Tf
0.7859 0 TD
(\))Tj
/F13 1 Tf
6.9738 0 0 6.9738 541.755 524.118 Tm
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/F12 1 Tf
0.5213 0 TD
(})Tj
/F11 1 Tf
0.8248 0 TD
[(is)-325.6(cyclotomic.)-449.5(S)0.3(upp)51.3(o)-0.2(se)-324.1(also)-323.6(that)]TJ
/F6 1 Tf
-10.7322 -1.3 TD
(G)Tj
/F11 1 Tf
1.1437 0 TD
-0.0001 Tc
[(is)-359.1(a)-357.1(l)-0.2(ine)-358.6(g)0.1(r)51.2(aph.)-460.4(Then)]TJ
/F6 1 Tf
9.6219 0 TD
0 Tc
(G)Tj
/F11 1 Tf
1.1437 0 TD
[(is)-359(a)-357(S)0.3(alem)-358.4(gr)51.3(aph.)]TJ
-11.9093 -2.5999 TD
-0.0513 Tc
[(P)-51.4(roo)-51.5(f)-50.9(:)]TJ
/F2 1 Tf
3.2432 0 TD
-0.0002 Tc
[(Recall)-416.2(that)-416.2(a)-414.4(line)-416.7(g)0.2(raph)]TJ
/F6 1 Tf
11.1469 0 TD
0 Tc
(L)Tj
/F2 1 Tf
1.0958 0 TD
-0.0002 Tc
[(is)-416.1(obtained)-416.7(from)-415.3(an-)]TJ
-15.4858 -1.3 TD
-0.0001 Tc
[(other)-449.5(graph)]TJ
/F6 1 Tf
5.6814 0 TD
0 Tc
(H)Tj
/F2 1 Tf
1.3614 0 TD
-0.0001 Tc
[(b)27.9(y)-448.9(dening)-449.6(the)-449.1(v)28.1(ertices)-450.3(of)]TJ
/F6 1 Tf
12.2246 0 TD
0 Tc
(L)Tj
/F2 1 Tf
1.1292 0 TD
-0.0003 Tc
[(to)-449.8(b)-28.3(e)-449.3(the)]TJ
-20.3966 -1.3 TD
-0.0002 Tc
[(edges)-307.7(of)]TJ
/F6 1 Tf
3.7581 0 TD
0 Tc
(H)Tj
/F2 1 Tf
0.9124 0 TD
-0.0002 Tc
[(,)-312.3(with)-308.3(t)28.2(w)28.2(o)-308.7(v)28(e)-0.2(rtices)-307.7(of)]TJ
/F6 1 Tf
9.4097 0 TD
0 Tc
(L)Tj
/F2 1 Tf
0.9874 0 TD
-0.0002 Tc
[(adjacen)27.8(t)-307.8(i)0.2(f)-308(a)0.2(nd)-307.4(only)-307.1(if)]TJ
-15.0676 -1.3 TD
-0.0001 Tc
[(the)-356.1(c)-0.1(orresp)-28.1(onding)-354.7(edges)-355.5(of)]TJ
/F6 1 Tf
12.0485 0 TD
0 Tc
(H)Tj
/F2 1 Tf
1.2674 0 TD
-0.0002 Tc
[(are)-355.2(i)0.2(nciden)27.8(t)-356.6(a)0.2(t)-355.7(a)-354.8(common)]TJ
-13.3159 -1.3 TD
-0.0282 Tc
[(ve)-28.2(r)-28.6(t)-27.8(e)-28.2(x)-270.1(o)-27.8(f)]TJ
/F6 1 Tf
3.9866 0 TD
0 Tc
(H)Tj
/F2 1 Tf
0.9124 0 TD
-0.0002 Tc
[(.)-414.4(I)-0.4(t)-241(i)0.2(s)-242.6(k)0(no)28.2(wn)-243.2(that)-242.8(line)-243.2(g)0.2(raphs)-242.6(ha)28.2(v)28(e)-243.2(least)-241.9(e)-0.2(igen-)]TJ
-4.8991 -1.3 TD
-0.0001 Tc
[(v)55.2(alue)-381.3(o)0.3(f)-380.2(a)0.3(t)-380.9(l)0.3(east)]TJ
/F12 1 Tf
7.4719 0 TD
0 Tc
()Tj
/F2 1 Tf
0.7778 0 TD
-0.0002 Tc
[(2)-380.1([)0.2(Go)-27.8(dsil)-381(and)-380.5(R)-0.4(o)28.2(y)0(le)-382.3(00,)-392.7(Chapter)-381.8(12].)]TJ
-8.2497 -1.3 TD
[(The)-285.7(p)-0.2(ro)-27.8(of)-285.5(of)-285.5(this)-285.1(follo)28.2(ws)-287.8(easily)-286.4(from)-285.3(the)-285.7(f)0(act)-285.2(t)0.2(hat)-286.1(t)0.2(he)-285.7(ad-)]TJ
T*
[(jacency)-318.9(matrix)]TJ
/F6 1 Tf
6.779 0 TD
0 Tc
(A)Tj
/F2 1 Tf
1.0678 0 TD
-0.0004 Tc
(of)Tj
/F6 1 Tf
1.1247 0 TD
0 Tc
(L)Tj
/F2 1 Tf
0.9982 0 TD
-0.0003 Tc
[(is)-319.5(giv)27.9(en)-320.1(b)27.7(y)]TJ
/F6 1 Tf
4.9614 0 TD
0 Tc
(A)Tj
/F2 1 Tf
0.9422 0 TD
0.1925 Tc
(+2)Tj
/F6 1 Tf
1.4698 0 TD
0 Tc
(I)Tj
/F2 1 Tf
0.7968 0 TD
(=)Tj
/F6 1 Tf
1.0552 0 TD
(B)Tj
/F14 1 Tf
6.9738 0 0 6.9738 262.296 335.4601 Tm
(T)Tj
/F6 1 Tf
9.9626 0 0 9.9626 268.569 331.851 Tm
(B)Tj
/F2 1 Tf
0.8094 0 TD
0.0001 Tc
[(,)-320.2(w)0.5(here)]TJ
/F6 1 Tf
-21.4434 -1.3009 TD
0 Tc
(B)Tj
/F2 1 Tf
1.1365 0 TD
-0.0002 Tc
[(is)-328.5(the)-328.1(i)0.2(ncidence)-328.1(matrix)-329.7(of)]TJ
/F6 1 Tf
11.4242 0 TD
0 Tc
(H)Tj
/F2 1 Tf
0.9124 0 TD
-0.0002 Tc
[(.)-443.3(F)82.5(urther,)-327.7(b)27.8(y)-327.9(L)-0.3(emma)-328.6(2.1,)]TJ
/F6 1 Tf
-13.4731 -1.3 TD
0 Tc
(G)Tj
/F2 1 Tf
1.1193 0 TD
-0.0002 Tc
[(has)-333.9(o)0.2(ne)-334.5(eigen)27.8(v)55.1(alue)]TJ
/F6 1 Tf
8.3952 0 TD
0 Tc
()Tj
/F2 1 Tf
0.5836 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(G)Tj
/F2 1 Tf
0.7859 0 TD
(\))Tj
/F6 1 Tf
0.6667 0 TD
(>)Tj
/F2 1 Tf
1.0561 0 TD
-0.0004 Tc
(2.)Tj
ET
301.302 312.524 m
308.079 312.524 l
301.504 306.345 m
301.504 312.33 l
307.885 306.345 m
307.885 312.33 l
301.302 306.152 m
308.079 306.152 l
S
BT
9.9626 0 0 9.9626 74.952 288.822 Tm
-0.0001 Tc
[(T)83.4(o)-495.6(use)-495.2(t)0.3(his)-496.4(r)-0.5(esult)-494.7(c)-0.1(onstructiv)28.1(ely)83.2(,)-538.1(rst)-494.7(note)-496.1(that)-496.5(all)]TJ
-1.1997 -1.3 TD
[(paths)-481.9(a)0.3(nd)-480.7(cycles)-481.9(are)-480.7(line)-481.6(g)0.3(raphs,)-518.2(a)0.3(s)-481(w)28.3(ell)-482.1(a)0.3(s)-481(b)-28.1(eing)-481.2(cy-)]TJ
T*
-0.0002 Tc
[(clotomic.)-713.4(T)0.2(hen)-423(tak)28(e)-423(a)0.2(n)27.8(y)-423.7(graph)]TJ
/F6 1 Tf
14.5129 0 TD
0 Tc
(H)Tj
/F2 1 Tf
1.3352 0 TD
-0.0001 Tc
[(consisting)-423.4(o)0.3(f)-421.8(o)0.3(ne)-422.9(or)]TJ
-15.8481 -1.3 TD
-0.0002 Tc
[(t)28.2(w)28.2(o)-437(connected)-436.6(comp)-28.2(onen)27.8(ts,)-463.2(e)-0.2(ac)27.8(h)-436.6(o)0.2(f)-436.3(w)0.2(hic)27.8(h)-437.5(is)-436(a)-436.1(p)-0.2(ath)-436.6(or)]TJ
T*
[(cycle,)-400(and)-386.9(a)0.2(dd)-387.8(to)]TJ
/F6 1 Tf
8.0862 0 TD
0 Tc
(H)Tj
/F2 1 Tf
1.2991 0 TD
-0.0001 Tc
[(an)-386.8(extra)-386.3(edge)-386.8(j)0.1(oining)-388.1(a)0.3(n)27.9(y)-387.4(t)28.3(w)28.3(o)-387.2(dis-)]TJ
-9.3853 -1.3 TD
[(tinct)-412.5(nonadjacen)27.9(t)-412.5(v)28.1(ertices.)-678.1(T)0.3(hen)-412.1(the)-411.2(line)-412.1(g)0.3(raph)-412.1(of)-411.8(this)]TJ
T*
-0.0002 Tc
[(augmen)27.8(t)0.2(ed)-308.3(graph,)-311.4(if)-307.1(not)-306(again)-308.3(cyclotomic,)-314.1(will)-306.9(b)-28.2(e)-306.5(a)-306(n)-0.2(on-)]TJ
T*
[(bipartite)-335.4(Salem)-334(g)0.2(raph.)]TJ
/F3 1 Tf
0 -2.3452 TD
[(4.)-1201(LEMMAS)-278.9(O)-0.1(N)-278.3(R)0.1(ECIPROC)24.5(A)0.1(L)-280.7(P)0.2(OL)74.3(YNOMIALS)]TJ
2.0344 -1.2006 TD
[(OF)-278(GRAPHS)]TJ
/F2 1 Tf
-2.0344 -1.8998 TD
-0.0001 Tc
[(F)82.6(o)0.3(r)-361(t)0.3(he)-362.4(pro)-27.7(o)0.3(f)-361.2(o)0.3(f)-362.1(T)0.3(heorem)-361(1.1,)-370(w)28.3(e)-362.4(shall)-361(need)-361.5(to)-361.9(consider)]TJ
0 -1.3 TD
[(sp)-28.1(ecial)-413.4(families)-416(o)0.3(f)-413.6(g)0.3(raphs,)-433.3(o)0.3(btained)-414.8(b)27.9(y)-413.6(adding)-413.4(paths)-414.2(t)0.3(o)]TJ
T*
0 Tc
[(a)-388(g)0.4(raph.)-607.5(Here)-387.6(w)28.4(e)-387.6(establish)-389.4(t)0.4(he)-387.6(general)-388(structure)-387.6(o)0.4(f)-388.2(t)0.4(he)]TJ
T*
-0.0002 Tc
[(recipro)-27.8(c)-0.2(al)-343(p)-28.2(olynomials)-345.6(of)-342.4(suc)27.8(h)-342.6(families)-344.7(a)0.2(nd)-343.5(sho)28.2(w)-343.1(ho)28.2(w)-343.1(i)0.2(n)]TJ
T*
-0.0001 Tc
[(certain)-338.9(cases)-339.2(o)0.3(ne)-338.9(can)-338.9(r)-0.5(etriev)28.1(e)-338.9(a)-338.4(Pisot)-339.3(n)27.9(um)28.3(b)-28.1(e)-0.1(r)-338.4(f)0.1(rom)-339.4(a)-338.4(se-)]TJ
T*
[(quence)-333.5(of)-334.1(graph)-333.5(S)-0.1(alem)-334.8(n)27.9(um)28.3(b)-28.1(e)-0.1(rs.)]TJ
27.5999 63.8 TD
-0.0002 Tc
[(Throughout)-443.3(this)-443.2(section,)-469.5(r)-0.6(ecipro)-27.8(c)-0.2(al)-442.4(p)-28.2(olynomials)-445(will)]TJ
-1.1997 -1.3 TD
[(b)-28.2(e)-537.7(written)-540.4(a)0.2(s)-538.9(f)0(unctions)-539.9(o)0.2(f)-539.3(a)-538.2(v)55.1(a)0.2(riable)]TJ
/F6 1 Tf
17.5636 0 TD
0 Tc
(z)Tj
/F2 1 Tf
0.5095 0 TD
-0.0001 Tc
[(,)-588.7(a)0.3(nd)-539.4(w)28.3(e)-539.4(con-)]TJ
-18.0731 -1.2999 TD
-0.0002 Tc
[(v)28(enien)27.8(tly)-430(treat)-428.9(t)0.2(he)-428.4(bipartite)-430.2(and)-429.3(n)-0.2(on)27.8(bipartite)-430.2(cases)-428.7(to-)]TJ
T*
[(gether)-389.1(b)27.8(y)-388.4(writing)]TJ
/F6 1 Tf
8.0582 0 TD
0 Tc
(y)Tj
/F2 1 Tf
0.8953 0 TD
(=)Tj
/F12 1 Tf
1.1463 0.72 TD
()Tj
ET
434.934 683.297 m
440.01 683.297 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 434.9341 675.921 Tm
(z)Tj
/F2 1 Tf
0.8971 0 TD
-0.0002 Tc
[(if)-388.4(the)-388.7(g)0.2(raph)-388.7(is)-389(bipartite,)-403.6(a)0.2(nd)]TJ
/F6 1 Tf
-11.8297 -1.3 TD
0 Tc
(y)Tj
/F2 1 Tf
0.804 0 TD
(=)Tj
/F6 1 Tf
1.0552 0 TD
(z)Tj
/F2 1 Tf
0.8429 0 TD
-0.0001 Tc
(otherwise.)Tj
/F3 1 Tf
-2.702 -2.5999 TD
-0.0002 Tc
[(Lemma)-270.8(4.1.)]TJ
/F11 1 Tf
5.4456 0 TD
-0.0518 Tc
[(Le)-51.6(t)]TJ
/F6 1 Tf
1.7137 0 TD
0 Tc
(G)Tj
/F11 1 Tf
1.131 0 TD
[(b)51.7(e)-345.8(a)-345.3(g)0.2(r)51.3(aph)-345.3(with)-344.4(a)-345.3(d)-0.2(istinguishe)51.7(d)-346.2(vertex)]TJ
/F6 1 Tf
-8.2904 -1.2999 TD
(v)Tj
/F11 1 Tf
0.5213 0 TD
0.8361 Tc
[(.F)912.5(o)835.9(r)352.6(e)887.8(a)835.9(c)836.3(h)]TJ
/F6 1 Tf
5.5097 0 TD
0 Tc
(m)Tj
/F12 1 Tf
1.384 0 TD
()Tj
/F2 1 Tf
1.2837 0 TD
(0)Tj
/F11 1 Tf
0.4996 0 TD
0.5154 Tc
[(,l)515.3(e)515.6(t)]TJ
/F6 1 Tf
2.3533 0 TD
0 Tc
(G)Tj
/F14 1 Tf
6.9738 0 0 6.9738 448.929 622.623 Tm
(m)Tj
/F11 1 Tf
9.9626 0 0 9.9626 461.313 624.1171 Tm
[(b)51.7(e)-484(the)-483.1(gr)51.3(aph)-483.5(obtaine)51.7(d)-484.4(b)0.2(y)]TJ
-13.5804 -1.3 TD
[(attaching)-296.1(one)-296.1(e)0.2(ndvertex)-296.8(o)-0.2(f)-295.9(a)-0.2(n)]TJ
/F6 1 Tf
13.0232 0 TD
(m)Tj
/F11 1 Tf
0.8781 0 TD
0.0001 Tc
[(-vertex)-295.8(p)51.4(ath)-295.5(to)-296.4(the)-295.1(vertex)]TJ
/F6 1 Tf
-13.9013 -1.3 TD
0 Tc
(v)Tj
/F11 1 Tf
0.8781 0 TD
0.0004 Tc
(\(so)Tj
/F6 1 Tf
1.6866 0 TD
0 Tc
(G)Tj
/F14 1 Tf
6.9738 0 0 6.9738 359.397 596.721 Tm
(m)Tj
/F11 1 Tf
9.9626 0 0 9.9626 370.53 598.215 Tm
0.0002 Tc
(has)Tj
/F6 1 Tf
1.7896 0 TD
0 Tc
(m)Tj
/F11 1 Tf
1.2358 0 TD
[(mor)51.3(e)-357.6(vertic)51.7(e)0.2(s)-359(than)]TJ
/F6 1 Tf
8.4078 0 TD
(G)Tj
/F11 1 Tf
0.7859 0 TD
0.0004 Tc
(\).)Tj
-15.4876 -1.3 TD
-0.0518 Tc
[(Le)-51.6(t)]TJ
/F6 1 Tf
1.7688 0 TD
0 Tc
(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 363.159 583.77 Tm
(m)Tj
/F2 1 Tf
9.9626 0 0 9.9626 370.728 585.264 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.5095 0 TD
(\))Tj
/F11 1 Tf
0.7896 0 TD
[(b)51.7(e)-400.9(the)-400.9(r)51.3(e)51.7(cipr)51.3(o)51.3(c)51.7(al)-402.1(p)51.3(o)-0.2(lynomial)-402.1(of)]TJ
/F6 1 Tf
13.7342 0 TD
(G)Tj
/F14 1 Tf
6.9738 0 0 6.9738 532.197 583.77 Tm
(m)Tj
/F11 1 Tf
9.9626 0 0 9.9626 539.766 585.264 Tm
0.5895 Tc
[(.T)589.6(h)589.3(e)589.7(n)]TJ
-21.4552 -1.3 TD
-0.0001 Tc
(for)Tj
/F6 1 Tf
1.5972 0 TD
0 Tc
(m)Tj
/F18 1 Tf
1.1554 0 TD
()Tj
/F2 1 Tf
1.0561 0 TD
(2)Tj
/F11 1 Tf
0.8573 0 TD
0.0002 Tc
[(we)-357.4(have)]TJ
/F2 1 Tf
-0.1464 -2.0967 TD
0 Tc
(\()Tj
/F6 1 Tf
0.3885 0 TD
(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 380.16 555.546 Tm
(2)Tj
/F12 1 Tf
9.9626 0 0 9.9626 386.847 551.424 Tm
()Tj
/F2 1 Tf
1 0 TD
-0.0004 Tc
(1\))Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 413.226 549.9301 Tm
(m)Tj
/F2 1 Tf
9.9626 0 0 9.9626 420.795 551.424 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.5095 0 TD
0.2778 Tc
(\)=)Tj
/F6 1 Tf
1.7218 0 TD
0 Tc
(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 452.142 555.546 Tm
(2)Tj
/F14 1 Tf
0.5691 0 TD
(m)Tj
/F6 1 Tf
9.9626 0 0 9.9626 463.68 551.424 Tm
(P)Tj
/F2 1 Tf
0.7814 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.5095 0 TD
(\))Tj
/F12 1 Tf
0.6107 0 TD
()Tj
/F6 1 Tf
1 0 TD
(P)Tj
/F15 1 Tf
6.9738 0 0 6.9738 504.243 555.546 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 508.815 551.424 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.5095 0 TD
(\))Tj
/F6 1 Tf
0.5547 0 TD
(,)Tj
/F11 1 Tf
-19.8011 -2.0958 TD
-0.0001 Tc
[(for)-334.6(s)-0.4(ome)-334.2(m)0.1(onic)-335.1(inte)51.6(ger)-336.4(p)51.2(o)-0.3(lynomial)]TJ
/F6 1 Tf
15.3955 0 TD
0 Tc
(P)Tj
/F2 1 Tf
0.7814 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.5095 0 TD
(\))Tj
/F11 1 Tf
0.7227 0 TD
0.0001 Tc
[(that)-333.5(dep)51.4(e)0.3(nds)-335.4(o)-0.1(n)]TJ
/F6 1 Tf
-17.7976 -1.3 TD
0 Tc
(G)Tj
/F11 1 Tf
1.1437 0 TD
-0.0001 Tc
(and)Tj
/F6 1 Tf
1.9423 0 TD
0 Tc
(v)Tj
/F11 1 Tf
0.8781 0 TD
0.0001 Tc
[(but)-357.9(n)0.4(ot)-357.9(on)]TJ
/F6 1 Tf
4.8819 0 TD
0 Tc
(m)Tj
/F11 1 Tf
0.8781 0 TD
0.3573 Tc
[(,a)357.1(n)357.6(d)-0.6(w)356.8(i)357.7(t)357.1(h)]TJ
/F6 1 Tf
4.778 0 TD
0 Tc
(P)Tj
/F15 1 Tf
6.9738 0 0 6.9738 478.278 521.2111 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 482.859 517.593 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.5095 0 TD
0.2778 Tc
(\)=)Tj
/F6 1 Tf
1.7218 0 TD
0 Tc
(z)Tj
/F13 1 Tf
6.9738 0 0 6.9738 514.035 521.2111 Tm
0.0003 Tc
(deg)Tj
/F14 1 Tf
1.9191 0 TD
0 Tc
(P)Tj
/F6 1 Tf
9.9626 0 0 9.9626 534.06 517.593 Tm
(P)Tj
/F2 1 Tf
0.7814 0 TD
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
(/z)Tj
/F2 1 Tf
1.0091 0 TD
0 Tc
(\))Tj
/F11 1 Tf
0.3885 0 TD
(.)Tj
-23.9494 -2.5999 TD
-0.0513 Tc
[(P)-51.4(roo)-51.5(f)-50.9(:)]TJ
/F2 1 Tf
3.048 0 TD
0.0001 Tc
(Let)Tj
/F6 1 Tf
1.6948 0 TD
0 Tc
()Tj
/F14 1 Tf
6.9738 0 0 6.9738 379.503 489.234 Tm
(m)Tj
/F2 1 Tf
9.9626 0 0 9.9626 387.063 491.691 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
()Tj
/F2 1 Tf
0.5836 0 TD
-0.0002 Tc
[(\))-236.4(b)-28.2(e)-236(t)0.2(he)-236(c)27.8(h)-0.2(aracteristic)-237.8(p)-28.2(olynomial)-238.3(of)]TJ
/F6 1 Tf
15.6765 0 TD
0 Tc
(G)Tj
/F14 1 Tf
6.9738 0 0 6.9738 560.754 490.197 Tm
(m)Tj
/F2 1 Tf
9.9626 0 0 9.9626 568.323 491.691 Tm
(.)Tj
-24.3216 -1.3 TD
-0.0001 Tc
[(Then)-444.6(expanding)-445.9(this)-444.9(determinan)27.9(t)-445.9(along)-445.9(t)0.3(he)-445.5(ro)28.3(w)-444.1(c)-0.1(orre-)]TJ
T*
[(sp)-28.1(onding)-426.1(to)-426.1(the)-426.5(v)28.1(ertex)-427.2(a)0.3(t)-426.1(t)0.3(he)-426.5(lo)-27.7(ose)-427(endv)28.1(ertex)-426.3(o)0.3(f)-427.2(t)0.3(he)]TJ
T*
-0.0003 Tc
[(attac)27.7(hed)-335.5(path)-334.6(\(that)-335(whic)27.7(h)-334.6(i)0.1(s)-334(n)-0.3(ot)]TJ
/F6 1 Tf
14.6168 0 TD
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(v)Tj
/F2 1 Tf
0.5213 0 TD
-0.0002 Tc
[(\))-333.1(w)28.2(e)-333.6(g)0.2(et)-334(\(for)]TJ
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()Tj
/F2 1 Tf
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-0.0004 Tc
(2\))Tj
/F6 1 Tf
-15.7226 -2.0958 TD
0 Tc
()Tj
/F14 1 Tf
6.9738 0 0 6.9738 406.044 429.492 Tm
(m)Tj
/F2 1 Tf
9.9626 0 0 9.9626 416.376 431.958 Tm
(=)Tj
/F6 1 Tf
1.0552 0 TD
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()Tj
/F14 1 Tf
6.9738 0 0 6.9738 438.939 429.303 Tm
0 Tc
(m)Tj
/F15 1 Tf
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()Tj
/F13 1 Tf
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(1)Tj
/F12 1 Tf
9.9626 0 0 9.9626 458.91 431.958 Tm
()Tj
/F6 1 Tf
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()Tj
/F14 1 Tf
6.9738 0 0 6.9738 475.11 429.303 Tm
(m)Tj
/F15 1 Tf
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/F6 1 Tf
9.9626 0 0 9.9626 494.532 431.958 Tm
(.)Tj
/F2 1 Tf
-16.9148 -2.0958 TD
[(Recognising)-323(t)0.4(his)-321.9(a)0.4(s)-321.9(a)-322.1(Cheb)28(yshev)-321.4(recurrence,)-323(or)-322(using)-322.1(i)0.4(n-)]TJ
0 -1.3 TD
-0.0002 Tc
[(duction,)-326.8(w)28.2(e)-324.5(g)0.2(et)-325(\(up)-28.2(o)0.2(n)-324.5(r)-0.6(eplacing)]TJ
/F6 1 Tf
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()Tj
/F2 1 Tf
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(by)Tj
/F6 1 Tf
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(y)Tj
/F2 1 Tf
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/F6 1 Tf
1.4806 0 TD
-0.0004 Tc
(/y)Tj
/F2 1 Tf
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[(and)-324.6(m)28.1(ulti-)]TJ
-20.0262 -1.3 TD
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[(plying)-333.9(through)-334.4(b)27.9(y)-334.1(t)0.3(he)-333.5(appropriate)-335.3(p)-28.1(o)28.3(w)28.3(e)-0.1(r)-333.8(o)0.3(f)]TJ
/F6 1 Tf
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(y)Tj
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(\))Tj
/F6 1 Tf
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(R)Tj
/F14 1 Tf
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(m)Tj
/F2 1 Tf
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(\()Tj
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0.3885 0 TD
(z)Tj
/F2 1 Tf
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0.2778 Tc
(\)=)Tj
/F6 1 Tf
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(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 381.96 368.5261 Tm
-0.0003 Tc
(2\()Tj
/F14 1 Tf
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/F13 1 Tf
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(+1\))Tj
/F12 1 Tf
9.9626 0 0 9.9626 407.961 364.917 Tm
0 Tc
()Tj
/F2 1 Tf
1 0 TD
(1)Tj
ET
376.713 360.665 m
422.91 360.665 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 386.37 351.3361 Tm
(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 391.617 354.2161 Tm
(2)Tj
/F12 1 Tf
9.9626 0 0 9.9626 398.295 351.3361 Tm
()Tj
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1 0 TD
(1)Tj
/F6 1 Tf
1.5899 0.6866 TD
(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 431.667 356.682 Tm
(m)Tj
/F15 1 Tf
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/F2 1 Tf
9.9626 0 0 9.9626 448.47 358.1761 Tm
(\()Tj
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(\))Tj
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()Tj
/F6 1 Tf
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(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 479.907 368.5261 Tm
(2)Tj
/F14 1 Tf
0.5691 0 TD
(t)Tj
/F12 1 Tf
9.9626 0 0 9.9626 489.591 364.917 Tm
()Tj
/F2 1 Tf
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(1)Tj
ET
474.66 360.665 m
504.54 360.665 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 476.163 351.3361 Tm
(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 481.41 354.2161 Tm
(2)Tj
/F12 1 Tf
9.9626 0 0 9.9626 488.088 351.3361 Tm
()Tj
/F2 1 Tf
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(1)Tj
/F6 1 Tf
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(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 510.975 362.289 Tm
(2)Tj
/F6 1 Tf
9.9626 0 0 9.9626 515.448 358.1761 Tm
(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 523.017 356.682 Tm
(m)Tj
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()Tj
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/F2 1 Tf
9.9626 0 0 9.9626 550.0079 358.1761 Tm
(\()Tj
/F6 1 Tf
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(z)Tj
/F2 1 Tf
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(\))Tj
-23.3812 -2.4707 TD
-0.0003 Tc
[(for)-334.1(a)0.1(n)27.7(y)]TJ
/F6 1 Tf
3.4193 0 TD
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(t)Tj
/F2 1 Tf
0.6947 0 TD
[(b)-28(e)0(t)28.4(w)28.4(een)-334.3(1)-332.9(a)0.4(nd)]TJ
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(m)Tj
/F12 1 Tf
1.1003 0 TD
()Tj
/F2 1 Tf
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-0.0002 Tc
[(1.)-444.2(T)83.3(a)0.2(king)]TJ
/F6 1 Tf
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(t)Tj
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(=)Tj
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(m)Tj
/F12 1 Tf
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()Tj
/F2 1 Tf
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-0.0002 Tc
[(1)-333.1(giv)28(es)]TJ
/F6 1 Tf
-19.2593 -2.655 TD
0 Tc
(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 352.953 305.616 Tm
(m)Tj
/F2 1 Tf
9.9626 0 0 9.9626 360.513 307.11 Tm
(\()Tj
/F6 1 Tf
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(z)Tj
/F2 1 Tf
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0.2778 Tc
(\)=)Tj
/F6 1 Tf
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/F13 1 Tf
6.9738 0 0 6.9738 393.057 317.469 Tm
(2)Tj
/F14 1 Tf
0.5691 0 TD
(m)Tj
/F12 1 Tf
9.9626 0 0 9.9626 406.809 313.851 Tm
()Tj
/F2 1 Tf
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(1)Tj
ET
387.81 309.608 m
421.749 309.608 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 391.347 300.2791 Tm
(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 396.594 303.15 Tm
(2)Tj
/F12 1 Tf
9.9626 0 0 9.9626 403.272 300.2791 Tm
()Tj
/F2 1 Tf
1 0 TD
(1)Tj
/F6 1 Tf
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(R)Tj
/F13 1 Tf
6.9738 0 0 6.9738 430.515 305.616 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 434.979 307.11 Tm
(\()Tj
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(\))Tj
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()Tj
/F6 1 Tf
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(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 466.425 317.469 Tm
-0.0003 Tc
(2\()Tj
/F14 1 Tf
1.0157 0 TD
0 Tc
(m)Tj
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()Tj
/F13 1 Tf
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(1\))Tj
/F12 1 Tf
9.9626 0 0 9.9626 496.593 313.851 Tm
0 Tc
()Tj
/F2 1 Tf
1 0 TD
(1)Tj
ET
461.178 309.608 m
511.542 309.608 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 472.923 300.2791 Tm
(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 478.17 303.15 Tm
(2)Tj
/F12 1 Tf
9.9626 0 0 9.9626 484.848 300.2791 Tm
()Tj
/F2 1 Tf
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(1)Tj
/F6 1 Tf
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(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 517.977 311.223 Tm
(2)Tj
/F6 1 Tf
9.9626 0 0 9.9626 522.441 307.11 Tm
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6.9738 0 0 6.9738 530.01 305.616 Tm
(0)Tj
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9.9626 0 0 9.9626 534.474 307.11 Tm
(\()Tj
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(.)Tj
/F2 1 Tf
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(1)Tj
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9.9626 0 0 9.9626 406.251 281.937 Tm
(\()Tj
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6.9738 0 0 6.9738 438.813 280.443 Tm
(0)Tj
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9.9626 0 0 9.9626 443.277 281.937 Tm
(\()Tj
/F6 1 Tf
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(z)Tj
/F2 1 Tf
0.5095 0 TD
0.0001 Tc
[(\))-332.8(w)28.5(e)-334.2(a)0.5(re)-333.3(done.)]TJ
ET
564.318 288.521 m
571.095 288.521 l
564.521 282.342 m
564.521 288.327 l
570.901 282.342 m
570.901 288.327 l
564.318 282.149 m
571.095 282.149 l
S
BT
9.9626 0 0 9.9626 337.968 261.0571 Tm
-0.0002 Tc
[(An)-461.8(easy)-460.7(induction)-463.7(extends)-461.3(this)-462.2(lemma)-463.2(to)-461.4(deal)-462.3(with)]TJ
-1.1997 -1.3 TD
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[(an)27.9(y)-334.1(n)27.9(um)28.3(b)-28.1(e)-0.1(r)-333.8(o)0.3(f)-334.1(a)0.3(dded)-333.5(p)-28.1(endan)27.9(t)-333.9(paths.)]TJ
/F3 1 Tf
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[(Lemma)-352.1(4.2.)]TJ
/F11 1 Tf
5.75 0 TD
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[(Le)-51.6(t)]TJ
/F6 1 Tf
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[(b)51.8(e)-425.2(a)-424.7(g)0.3(r)51.4(aph)-424.7(and)]TJ
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6.9738 0 0 6.9738 491.958 220.7101 Tm
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9.9626 0 0 9.9626 496.422 222.204 Tm
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6.9738 0 0 6.9738 523.386 220.7101 Tm
0 Tc
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 528.291 222.204 Tm
(\))Tj
/F11 1 Tf
0.8139 0 TD
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[(al)425.2(i)425.7(s)425(to)425.1(f)]TJ
-21.1173 -1.3 TD
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[(\(not)-479.9(ne)51.7(c)51.7(e)0.2(ssarily)-481.1(distinct\))-480.9(vertic)51.7(e)0.2(s)-481.8(o)-0.2(f)]TJ
/F6 1 Tf
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/F11 1 Tf
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[(.L)879.8(e)828.2(t)]TJ
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6.9738 0 0 6.9738 536.382 207.759 Tm
(m)Tj
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6.9738 0 0 6.9738 547.344 207.759 Tm
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4.9813 0 0 4.9813 566.244 206.706 Tm
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9.9626 0 0 9.9626 326.016 196.302 Tm
[(b)51.7(e)-503.9(the)-503.9(gr)51.3(aph)-503.4(obtaine)51.7(d)-505.2(b)0.2(y)-503.6(attaching)-503.9(one)-503.9(e)0.2(ndvertex)-504.5(o)-0.2(f)-503.7(a)]TJ
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(i)Tj
/F11 1 Tf
9.9626 0 0 9.9626 358.542 183.351 Tm
[(-vertex)-368.1(p)51.3(ath)-367.9(to)-367(vertex)]TJ
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(i)Tj
/F11 1 Tf
9.9626 0 0 9.9626 466.812 183.351 Tm
0.0004 Tc
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/F6 1 Tf
1.6966 0 TD
0 Tc
(G)Tj
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6.9738 0 0 6.9738 491.544 181.857 Tm
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 498.618 180.858 Tm
(1)Tj
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6.9738 0 0 6.9738 502.506 181.857 Tm
0.0001 Tc
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4.9813 0 0 4.9813 521.415 180.804 Tm
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9.9626 0 0 9.9626 529.92 183.351 Tm
0.0002 Tc
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6.9738 0 0 6.9738 556.596 181.857 Tm
(1)Tj
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9.9626 0 0 9.9626 563.3459 183.351 Tm
(+)Tj
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(...)Tj
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6.9738 0 0 6.9738 358.452 168.906 Tm
(k)Tj
/F11 1 Tf
9.9626 0 0 9.9626 366.885 170.4001 Tm
[(mor)51.3(e)-355.8(vertic)51.7(e)0.2(s)-356.3(than)]TJ
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[(\).)-458.2(L)52.1(e)0.5(t)]TJ
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2.8981 0 TD
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(R)Tj
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6.9738 0 0 6.9738 494.847 168.906 Tm
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 501.921 167.907 Tm
(1)Tj
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6.9738 0 0 6.9738 505.8 168.906 Tm
0.0001 Tc
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/F21 1 Tf
4.9813 0 0 4.9813 524.709 167.8531 Tm
0 Tc
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 529.56 170.4001 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
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(\))Tj
/F11 1 Tf
0.7435 0 TD
0.0002 Tc
[(b)51.9(e)-355.6(the)]TJ
-22.0722 -1.3 TD
-0.0514 Tc
[(rec)-51.2(i)-51(p)-51.6(roca)-51.6(l)-515.8(po)-51.6(l)-51.5(y)-51(n)-51.1(o)-51.6(m)-51.2(i)-51(a)-51.6(l)-514.9(o)-51.6(f)]TJ
/F6 1 Tf
10.9463 0 TD
0 Tc
(G)Tj
/F14 1 Tf
6.9738 0 0 6.9738 442.899 155.9551 Tm
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 449.973 154.956 Tm
(1)Tj
/F14 1 Tf
6.9738 0 0 6.9738 453.861 155.9551 Tm
-0.0001 Tc
(,...,m)Tj
/F21 1 Tf
4.9813 0 0 4.9813 472.761 154.902 Tm
0 Tc
(k)Tj
/F11 1 Tf
9.9626 0 0 9.9626 477.612 157.449 Tm
0.0001 Tc
[(.)-775.5(T)0.2(hen)-463(i)0.5(f)-462.9(a)-0.1(l)-51.5(l)-461.6(the)]TJ
/F6 1 Tf
8.172 0 TD
0 Tc
(m)Tj
/F14 1 Tf
6.9738 0 0 6.9738 567.774 155.9551 Tm
(i)Tj
/F11 1 Tf
9.9626 0 0 9.9626 326.016 144.498 Tm
0.0002 Tc
[(ar)51.5(e)]TJ
/F18 1 Tf
1.6993 0 TD
0 Tc
()Tj
/F2 1 Tf
1.0552 0 TD
(2)Tj
/F11 1 Tf
0.8582 0 TD
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[(we)-357.4(have)]TJ
/F2 1 Tf
-3.4961 -2.0958 TD
0 Tc
(\()Tj
/F6 1 Tf
0.3885 0 TD
(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 336.294 127.731 Tm
(2)Tj
/F12 1 Tf
9.9626 0 0 9.9626 342.981 123.618 Tm
()Tj
/F2 1 Tf
1 0 TD
-0.0004 Tc
(1\))Tj
/F14 1 Tf
6.9738 0 0 6.9738 361.791 127.731 Tm
0 Tc
(k)Tj
/F6 1 Tf
9.9626 0 0 9.9626 366.696 123.618 Tm
(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 374.265 122.124 Tm
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 381.339 121.1251 Tm
(1)Tj
/F14 1 Tf
6.9738 0 0 6.9738 385.218 122.124 Tm
0.0001 Tc
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14.7179 0 TD
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()Tj
/F2 1 Tf
0.4978 0 TD
-0.0002 Tc
[(,)-424.3(w)28.2(e)-406.7(deduce)-405.8(that,)-425.3(for)]TJ
-15.2157 -1.3 TD
[(all)-328.6(large)-329.1(enough)]TJ
/F6 1 Tf
7.2641 0 TD
0 Tc
(m)Tj
/F2 1 Tf
0.8781 0 TD
(,)Tj
/F6 1 Tf
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/F14 1 Tf
6.9738 0 0 6.9738 135.63 389.496 Tm
(m)Tj
/F2 1 Tf
9.9626 0 0 9.9626 146.457 390.9901 Tm
-0.0002 Tc
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/F6 1 Tf
1.9387 0 TD
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[(ha)28.2(v)28(e)-329(the)-328.1(s)-0.5(ame)-329(n)27.8(u)-0.2(m)28.2(b)-28.2(er)-328.5(of)]TJ
-13.6419 -1.3 TD
[(zeros)-374.5(\(namely)-376.7(one\))-374.7(within)-376(that)-375.6(disc,)-385.5(a)0.2(nd)-374.2(hence)]TJ
/F6 1 Tf
21.2142 0 TD
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()Tj
/F14 1 Tf
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(m)Tj
/F12 1 Tf
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()Tj
/F6 1 Tf
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()Tj
/F2 1 Tf
-24.103 -1.3 TD
-0.0004 Tc
(as)Tj
/F6 1 Tf
1.1943 0 TD
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(m)Tj
/F12 1 Tf
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0.2774 Tc
()Tj
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-0.0002 Tc
[(.)-433.4(S)-0.2(ince)-301(the)-300.1(e)-0.2(igen)27.8(v)55.1(alues)-302.3(of)-299.9(trivial)-302.4(Salem)-300.6(g)0.2(raphs)]TJ
-4.628 -1.3 TD
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[(form)-481.2(a)-481.2(d)-0.1(iscrete)-481.6(s)-0.4(et,)-518.2(w)28.3(e)-481.6(c)-0.1(an)-481.6(discard)-480.7(t)0.3(he)-481.6(at)-482.1(most)-481.2(nite)]TJ
T*
-0.0002 Tc
[(n)27.8(u)-0.2(m)28.2(b)-28.2(er)-416.2(of)-416.4(trivial)-417.1(Salem)-416.2(g)0.2(raphs)-416.1(in)-415.8(our)-416.2(s)-0.5(equence)-415.8(and)-415.8(s)-0.5(o)]TJ
T*
[(assume)-340.8(that)-342.1(all)-341.2(our)-341.2(S)-0.2(alem)-341.3(g)0.2(raphs)-341.1(are)-340.8(n)-0.2(on)27.8(trivial,)-345.8(so)-340.3(that)]TJ
T*
(the)Tj
/F6 1 Tf
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()Tj
/F14 1 Tf
6.9738 0 0 6.9738 62.415 311.79 Tm
(m)Tj
/F2 1 Tf
9.9626 0 0 9.9626 73.305 313.284 Tm
[(are)-333.4(S)0(alem)-334.7(n)28(um)28.4(b)-28(e)0(rs.)]TJ
-2.0525 -1.3 TD
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[(It)-458.6(remains)-459.4(t)0.3(o)-459.5(p)-0.1(ro)28.3(v)28.1(e)-459(that)]TJ
/F6 1 Tf
11.5263 0 TD
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()Tj
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[(is)-459.4(a)-458.6(P)0.2(isot)-459.5(n)27.9(u)-0.1(m)28.3(b)-28.1(er.)-820.8(T)0.3(he)]TJ
-13.6817 -1.3009 TD
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[(only)-298.2(alternativ)27.9(e)-300.2(w)28.1(ould)-298.4(b)-28.3(e)-297.5(that)]TJ
/F6 1 Tf
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()Tj
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[(is)-297.6(a)-296.9(S)-0.1(alem)-297.8(n)27.9(um)28.3(b)-28.1(e)-0.1(r.)-433.3(But)]TJ
-14.2545 -1.3 TD
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()Tj
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[(w)28.2(o)0.2(uld)-494.4(also)-493.9(b)-28.2(e)-491.7(a)-493(ro)-27.8(ot)-493(of)]TJ
/F6 1 Tf
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()Tj
/F2 1 Tf
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[(\),)-533.6(so)-492(w)28.3(o)0.3(uld)-494.3(b)-28.1(e)-492.5(a)]TJ
-16.9175 -1.3 TD
[(ro)-27.7(ot)-391.7(of)]TJ
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(m)Tj
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/F6 1 Tf
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(z)Tj
/F2 1 Tf
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[(\))-392(f)-0.2(or)-392.9(all)]TJ
/F6 1 Tf
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[(,)-406.4(giving)]TJ
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()Tj
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(m)Tj
/F2 1 Tf
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(=)Tj
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1.1527 0 TD
()Tj
/F2 1 Tf
0.8889 0 TD
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[(for)-392.9(all)]TJ
/F6 1 Tf
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/F2 1 Tf
0.8781 0 TD
-0.0002 Tc
[(.)-620.4(T)0.2(his)]TJ
-21.7524 -1.3 TD
[(con)27.8(t)0.2(radicts)-299.6(t)0.2(he)-297.4(fact)-298.8(that)-297.9(the)]TJ
/F6 1 Tf
12.5507 0 TD
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()Tj
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(m)Tj
/F2 1 Tf
9.9626 0 0 9.9626 180.828 248.52 Tm
-0.0001 Tc
[(are)-297.3(s)-0.4(trictly)-298(increasing)-297.8(as)]TJ
/F6 1 Tf
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0 Tc
(m)Tj
/F2 1 Tf
1.2114 0 TD
0.0001 Tc
(increases.)Tj
ET
0 0 0 1 K
0 J 0 j 0.405 w 10 M []0 d
1 i
279.216 242.153 m
285.993 242.153 l
279.418 235.974 m
279.418 241.959 l
285.79 235.974 m
285.79 241.959 l
279.216 235.781 m
285.993 235.781 l
S
BT
9.9626 0 0 9.9626 52.857 221.6281 Tm
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/F6 1 Tf
21.6198 0 TD
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()Tj
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-0.0004 Tc
(in)Tj
-23.7671 -1.3009 TD
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0 -1.3 TD
[(b)-28.2(e)-0.2(r,)-333.1(the)-333.6(p)-0.2(ro)-27.8(of)-334.2(sho)28.2(wing)-334(t)0.2(hat)-334.9(i)0.2(t)-334(i)0.2(s)-333.9(n)-0.2(ot)-334(conjugate)-335.4(to)-334(1)]TJ
/F6 1 Tf
22.3778 0 TD
-0.0004 Tc
(/)Tj
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0 Tc
(.)Tj
/F3 1 Tf
-23.3751 -2.5999 TD
-0.0002 Tc
[(Cor)17.5(o)0.2(llar)23.8(y)-473.1(4.4.)]TJ
/F11 1 Tf
7.1394 0 TD
0 Tc
[(With)-535.9(notation)-535.4(as)-536.1(in)-537.2(L)51.8(emma)-536.8(4.2,)-581.4(sup-)]TJ
-7.1394 -1.3 TD
0.0001 Tc
[(p)51.4(o)-0.1(se)-364.7(further)-364.2(that)]TJ
/F6 1 Tf
7.611 0 TD
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(G)Tj
/F11 1 Tf
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-0.0001 Tc
[(is)-365.4(c)51.6(o)-0.3(nne)51.6(cte)51.6(d)-367.1(and)-365.3(that)]TJ
/F6 1 Tf
9.612 0 TD
0 Tc
(G)Tj
/F14 1 Tf
6.9738 0 0 6.9738 231.786 155.3701 Tm
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 238.86 154.371 Tm
(1)Tj
/F14 1 Tf
6.9738 0 0 6.9738 242.739 155.3701 Tm
0.0001 Tc
(,...,m)Tj
/F21 1 Tf
4.9813 0 0 4.9813 261.648 154.317 Tm
0 Tc
(k)Tj
/F11 1 Tf
9.9626 0 0 9.9626 270.135 156.864 Tm
-0.0004 Tc
[(is)-364.8(a)]TJ
-23.009 -1.3 TD
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/F6 1 Tf
16.503 0 TD
(m)Tj
/F13 1 Tf
6.9738 0 0 6.9738 214.065 142.419 Tm
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 218.529 143.9131 Tm
0.1664 Tc
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/F14 1 Tf
6.9738 0 0 6.9738 249.408 142.419 Tm
0 Tc
(k)Tj
/F11 1 Tf
9.9626 0 0 9.9626 254.322 143.9131 Tm
0.6229 Tc
[(.T)623(h)622.7(e)623.1(n)]TJ
/F6 1 Tf
-21.4217 -1.3 TD
0 Tc
(G)Tj
/F14 1 Tf
6.9738 0 0 6.9738 48.735 129.468 Tm
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 55.809 128.469 Tm
(1)Tj
/F14 1 Tf
6.9738 0 0 6.9738 59.697 129.468 Tm
0.0001 Tc
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/F21 1 Tf
4.9813 0 0 4.9813 78.606 128.4151 Tm
0 Tc
(k)Tj
/F11 1 Tf
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-4.637 -1.3 TD
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/F6 1 Tf
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(m)Tj
/F13 1 Tf
6.9738 0 0 6.9738 81.243 116.517 Tm
(1)Tj
/F6 1 Tf
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0 Tc
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 121.509 118.011 Tm
(\))Tj
/F11 1 Tf
0.3885 0 TD
[(.)-603.9(F)76.4(urthermor)51.3(e,)]TJ
/F6 1 Tf
7.0545 0 TD
(P)Tj
/F13 1 Tf
6.9738 0 0 6.9738 202.059 116.211 Tm
0.0001 Tc
(\(1)Tj
/F14 1 Tf
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(,...,)Tj
/F13 1 Tf
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(1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 228.555 118.011 Tm
0 Tc
(\()Tj
/F6 1 Tf
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(z)Tj
/F2 1 Tf
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(\))Tj
/F11 1 Tf
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0.0002 Tc
[(,)-417.6(the)-405.2(le)51.9(ad-)]TJ
-20.1218 -1.3 TD
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[(ing)-285.4(p)51.2(olynomial)-284.8(o)-0.3(f)]TJ
/F6 1 Tf
7.6761 0 TD
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(R)Tj
/F14 1 Tf
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(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 132.021 102.567 Tm
(1)Tj
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0.0001 Tc
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4.9813 0 0 4.9813 154.809 102.5131 Tm
0 Tc
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 159.66 105.0601 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
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(\))Tj
/F11 1 Tf
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[(,)-299.5(i)0.4(s)-284.9(the)-283.5(pr)51.3(o)51.3(d)-0.2(uct)-284.8(o)-0.2(f)-284.1(the)-283.5(min-)]TJ
-13.2065 -1.3 TD
[(imal)-356.9(p)51.3(o)-0.2(lynomial)-357.8(of)-356.4(some)-355.8(Pisot)-357.1(n)0.3(umb)51.7(e)0.2(r)-358(\()]TJ
/F6 1 Tf
17.5772 0 TD
()Tj
/F11 1 Tf
0.4978 0 TD
0.0001 Tc
[(,)-355.4(s)-0.2(ay\),)-356.3(a)-356.9(p)51.4(ower)]TJ
-18.0749 -1.3 TD
0.0002 Tc
(of)Tj
/F6 1 Tf
1.1753 0 TD
0 Tc
(z)Tj
/F11 1 Tf
0.5095 0 TD
-0.0001 Tc
[(,)-357.4(a)-0.3(nd)-358(p)51.2(e)0.1(rhaps)-357.3(a)-358(c)0.1(yclotomic)-358.6(p)51.2(o)-0.3(lynomial.)]TJ
25.9151 63.8 TD
0.0001 Tc
[(Mor)51.4(e)51.8(over,)-412.3(i)0.5(f)-401.5(w)-0.4(e)-400.8(l)0(et)-401.2(al)-51.5(l)-401.1(the)]TJ
/F6 1 Tf
11.9283 0 TD
0 Tc
(m)Tj
/F14 1 Tf
6.9738 0 0 6.9738 443.457 713.28 Tm
(i)Tj
/F11 1 Tf
9.9626 0 0 9.9626 450.774 714.774 Tm
-0.0001 Tc
[(tend)-401.4(to)-401.4(innity)-402.6(in)-401.8(any)]TJ
-14.7404 -1.3 TD
0 Tc
[(manner)-371.5(\()-0.4(one)-371.1(a)-0.2(t)-370.6(a)-371.5(time,)-375.4(in)-371(bunches,)-375.4(or)-370.6(al)-51.6(l)-370.5(t)-0.2(o)51.3(gether,)-374.5(p)51.3(e)0.2(r-)]TJ
T*
0.0001 Tc
[(haps)-445.6(at)-445.5(varying)-446.9(r)51.4(ates\),)-467.4(the)-446(Salem)-446.9(n)0.4(umb)51.8(e)0.3(rs)]TJ
/F6 1 Tf
19.4625 0 TD
0 Tc
()Tj
/F14 1 Tf
6.9738 0 0 6.9738 502.173 687.3781 Tm
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 509.247 686.379 Tm
(1)Tj
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6.9738 0 0 6.9738 513.135 687.3781 Tm
-0.0001 Tc
(,...,m)Tj
/F21 1 Tf
4.9813 0 0 4.9813 532.035 686.325 Tm
0 Tc
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 541.251 688.8721 Tm
(=)Tj
/F6 1 Tf
-23.822 -1.3 TD
()Tj
/F2 1 Tf
0.5502 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(G)Tj
/F14 1 Tf
6.9738 0 0 6.9738 321.102 674.427 Tm
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 328.176 673.428 Tm
(1)Tj
/F14 1 Tf
6.9738 0 0 6.9738 332.064 674.427 Tm
0.0001 Tc
(,...,m)Tj
/F21 1 Tf
4.9813 0 0 4.9813 350.973 673.374 Tm
0 Tc
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 355.824 675.921 Tm
(\))Tj
/F11 1 Tf
0.7462 0 TD
[(tend)-357.9(to)]TJ
/F6 1 Tf
3.4247 0 TD
()Tj
/F11 1 Tf
0.4978 0 TD
(.)Tj
-9.8785 -1.9278 TD
-0.0513 Tc
[(P)-51.4(roo)-51.5(f)-50.9(:)]TJ
/F2 1 Tf
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-0.0001 Tc
[(Throughout)-399.9(w)28.3(e)-398.5(supp)-28.1(ose)-396.7(t)0.3(hat)-399(t)0.3(he)]TJ
/F6 1 Tf
15.0034 0 TD
0 Tc
(m)Tj
/F14 1 Tf
6.9738 0 0 6.9738 494.136 655.2211 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 501.417 656.715 Tm
-0.0001 Tc
[(are)-397.6(all)-399(suf-)]TJ
-19.8237 -1.3 TD
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[(cien)27.8(tly)-337(large)-336.3(so)-335.8(that)-335.8(all)-336.7(the)-336.3(g)0.2(raphs)-335.7(under)-335.8(consideration)]TJ
0 -1.3009 TD
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[(are)-266.6(S)-0.1(alem)-268(g)0.3(raphs.)-422.4(A)0.1(s)-266.9(i)0.3(n)-266.6(t)0.3(he)-267.5(pro)-27.7(o)0.3(f)-267.3(o)0.3(f)-266.4(t)0.3(he)-267.5(previous)-267.8(l)0.3(emma,)]TJ
0 -1.3 TD
[(w)28.3(e)-495.2(ma)28.3(y)-495(a)0.3(ssume)-495.2(that)-494.7(these)-494.3(a)0.3(re)-495.2(non)27.9(t)0.3(rivial,)-537.2(so)-493.8(that)-495.6(the)]TJ
/F6 1 Tf
T*
0 Tc
()Tj
/F14 1 Tf
6.9738 0 0 6.9738 308.277 603.408 Tm
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 315.351 602.4091 Tm
(1)Tj
/F14 1 Tf
6.9738 0 0 6.9738 319.23 603.408 Tm
0.0001 Tc
(,...,m)Tj
/F21 1 Tf
4.9813 0 0 4.9813 338.139 602.355 Tm
0 Tc
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 348.156 604.902 Tm
-0.0001 Tc
[(are)-518.7(S)-0.1(alem)-520(n)27.9(um)28.3(b)-28.1(e)-0.1(rs.)-1001.5(F)-0.5(ixing)]TJ
/F6 1 Tf
13.2779 0 TD
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(m)Tj
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6.9738 0 0 6.9738 489.186 603.408 Tm
(2)Tj
/F6 1 Tf
9.9626 0 0 9.9626 493.65 604.902 Tm
0.1664 Tc
(,...,m)Tj
/F14 1 Tf
6.9738 0 0 6.9738 524.529 603.408 Tm
0 Tc
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 534.609 604.902 Tm
-0.0004 Tc
(\(all)Tj
-23.1553 -1.3 TD
-0.0002 Tc
[(large)-424.8(enough\),)-447.8(a)0.2(nd)-423.9(letting)]TJ
/F6 1 Tf
12.0539 0 TD
0 Tc
(m)Tj
/F13 1 Tf
6.9738 0 0 6.9738 432.756 590.457 Tm
(1)Tj
/F12 1 Tf
9.9626 0 0 9.9626 441.486 591.951 Tm
0.4282 Tc
()Tj
/F2 1 Tf
2.4283 0 TD
-0.0002 Tc
[(,)-446.9(w)28.2(e)-424.8(a)0.2(pply)-424.6(L)-0.3(emma)]TJ
-16.2364 -1.3 TD
[(4.3)-458.7(to)-458.7(deduce)-458.2(that)]TJ
/F6 1 Tf
8.8324 0 TD
0 Tc
()Tj
/F14 1 Tf
6.9738 0 0 6.9738 396.27 577.506 Tm
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 403.344 576.507 Tm
(1)Tj
/F14 1 Tf
6.9738 0 0 6.9738 407.223 577.506 Tm
0.0001 Tc
(,...,m)Tj
/F21 1 Tf
4.9813 0 0 4.9813 426.132 576.453 Tm
0 Tc
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 435.546 579 Tm
-0.0001 Tc
[(tends)-458.4(to)-458.6(a)-458.6(P)0.2(isot)-458.6(n)27.9(u)-0.1(m)28.3(b)-28.1(er,)]TJ
-13.2119 -1.3 TD
0.0003 Tc
[(sa)28.7(y)]TJ
/F6 1 Tf
1.7273 0 TD
0 Tc
()Tj
/F15 1 Tf
6.9738 0 0 6.9738 325.809 564.5551 Tm
()Tj
/F14 1 Tf
1.1383 0 TD
0.0001 Tc
(,m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 343.188 563.556 Tm
0 Tc
(2)Tj
/F14 1 Tf
6.9738 0 0 6.9738 347.076 564.5551 Tm
0.0001 Tc
(,...,m)Tj
/F21 1 Tf
4.9813 0 0 4.9813 365.985 563.502 Tm
0 Tc
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 370.827 566.049 Tm
0.3338 Tc
[(,t)334.2(h)333.8(a)334.2(ti)334.2(sar)333.4(o)306.2(o)334.2(t)0.9(o)334.2(f)]TJ
/F23 1 Tf
-0.8862 -1.0136 TD
0 Tc
()Tj
/F14 1 Tf
6.9738 0 0 6.9738 343.917 534.108 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 347.238 533.109 Tm
(2)Tj
/F14 1 Tf
6.9738 0 0 6.9738 351.126 534.108 Tm
-0.0001 Tc
(,...,)Tj
/F21 1 Tf
4.9813 0 0 4.9813 366.273 533.0551 Tm
0 Tc
(k)Tj
/F15 1 Tf
6.9738 0 0 6.9738 370.629 534.108 Tm
0.0006 Tc
({)Tj
/F13 1 Tf
1.3564 0 TD
0 Tc
(0)Tj
/F14 1 Tf
0.5691 0 TD
(,)Tj
/F13 1 Tf
0.3394 0 TD
(1)Tj
/F15 1 Tf
0.5691 0 TD
(})Tj
/F6 1 Tf
9.9626 0 0 9.9626 396.135 546.483 Tm
(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 401.382 550.893 Tm
(2)Tj
/T1 1 Tf
0.009 0 0 -0.009 406.71 556.1221 Tm
()Tj
/F21 1 Tf
4.9813 0 0 4.9813 415.08 548.643 Tm
(i)Tj
/F24 1 Tf
0.533 0 TD
()Tj
/F22 1 Tf
1.0841 0 TD
(2)Tj
/F14 1 Tf
6.9738 0 0 6.9738 428.382 550.893 Tm
()Tj
/F21 1 Tf
4.9813 0 0 4.9813 431.703 549.894 Tm
(i)Tj
/F14 1 Tf
6.9738 0 0 6.9738 434.862 550.893 Tm
(m)Tj
/F21 1 Tf
4.9813 0 0 4.9813 441.936 549.894 Tm
(i)Tj
/F6 1 Tf
9.9626 0 0 9.9626 445.581 546.483 Tm
(P)Tj
/F13 1 Tf
6.9738 0 0 6.9738 451.98 544.683 Tm
0.0001 Tc
(\(1)Tj
/F14 1 Tf
1.0157 0 TD
(,)Tj
/F22 1 Tf
4.9813 0 0 4.9813 464.751 543.684 Tm
0 Tc
(2)Tj
/F14 1 Tf
6.9738 0 0 6.9738 468.639 544.683 Tm
-0.0001 Tc
(,...,)Tj
/F21 1 Tf
4.9813 0 0 4.9813 483.786 543.63 Tm
0 Tc
(k)Tj
/F13 1 Tf
6.9738 0 0 6.9738 488.142 544.683 Tm
(\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 491.751 546.483 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.5095 0 TD
(\))Tj
/F6 1 Tf
0.5547 0 TD
(.)Tj
/F2 1 Tf
-19.1064 -2.8393 TD
-0.0001 Tc
[(No)28.3(w)-354.7(w)28.3(e)-353.3(l)0.3(et)]TJ
/F6 1 Tf
5.2541 0 TD
0 Tc
(m)Tj
/F13 1 Tf
6.9738 0 0 6.9738 376.965 516.702 Tm
(2)Tj
/F12 1 Tf
9.9626 0 0 9.9626 384.534 518.196 Tm
0.3108 Tc
()Tj
/F2 1 Tf
2.3109 0 TD
-0.0001 Tc
[(,)-358.3(a)0.3(nd)-354.2(w)28.3(e)-354.2(get)-352.9(a)-353.8(sequence)-353.3(of)-354(Pisot)]TJ
-10.4024 -1.3 TD
[(n)27.9(u)-0.1(m)28.3(b)-28.1(ers)-333.8(t)0.3(hat)-333.9(c)-0.1(on)27.9(v)28.1(e)-0.1(rge)-334.4(t)0.3(o)-333.9(t)0.3(he)-334.4(unique)-333.5(r)-0.5(o)-27.7(o)0.3(t)-333.9(o)0.3(f)]TJ
/F23 1 Tf
5.5115 -0.8781 TD
0 Tc
()Tj
/F14 1 Tf
6.9738 0 0 6.9738 340.749 474.663 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 344.07 473.664 Tm
(3)Tj
/F14 1 Tf
6.9738 0 0 6.9738 347.958 474.663 Tm
-0.0001 Tc
(,...,)Tj
/F21 1 Tf
4.9813 0 0 4.9813 363.105 473.61 Tm
0 Tc
(k)Tj
/F15 1 Tf
6.9738 0 0 6.9738 367.461 474.663 Tm
0.0006 Tc
({)Tj
/F13 1 Tf
1.3564 0 TD
0 Tc
(0)Tj
/F14 1 Tf
0.5691 0 TD
(,)Tj
/F13 1 Tf
0.3394 0 TD
(1)Tj
/F15 1 Tf
0.5691 0 TD
(})Tj
/F6 1 Tf
9.9626 0 0 9.9626 392.967 487.029 Tm
(y)Tj
/F13 1 Tf
6.9738 0 0 6.9738 398.214 491.439 Tm
(2)Tj
/T1 1 Tf
0.009 0 0 -0.009 403.542 496.668 Tm
()Tj
/F21 1 Tf
4.9813 0 0 4.9813 411.912 489.198 Tm
(i)Tj
/F24 1 Tf
0.533 0 TD
()Tj
/F22 1 Tf
1.0841 0 TD
(3)Tj
/F14 1 Tf
6.9738 0 0 6.9738 425.214 491.439 Tm
()Tj
/F21 1 Tf
4.9813 0 0 4.9813 428.535 490.44 Tm
(i)Tj
/F14 1 Tf
6.9738 0 0 6.9738 431.685 491.439 Tm
(m)Tj
/F21 1 Tf
4.9813 0 0 4.9813 438.759 490.44 Tm
(i)Tj
/F6 1 Tf
9.9626 0 0 9.9626 442.413 487.029 Tm
(P)Tj
/F13 1 Tf
6.9738 0 0 6.9738 448.812 485.229 Tm
0.0001 Tc
(\(1)Tj
/F14 1 Tf
1.0157 0 TD
0 Tc
(,)Tj
/F13 1 Tf
0.3394 0 TD
(1)Tj
/F14 1 Tf
0.5691 0 TD
0.0001 Tc
(,)Tj
/F22 1 Tf
4.9813 0 0 4.9813 467.919 484.23 Tm
0 Tc
(3)Tj
/F14 1 Tf
6.9738 0 0 6.9738 471.807 485.229 Tm
0.0001 Tc
(,...,)Tj
/F21 1 Tf
4.9813 0 0 4.9813 486.963 484.176 Tm
0 Tc
(k)Tj
/F13 1 Tf
6.9738 0 0 6.9738 491.31 485.229 Tm
(\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 494.928 487.029 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.5095 0 TD
(\))Tj
/F6 1 Tf
0.5547 0 TD
(,)Tj
/F2 1 Tf
-20.625 -2.8393 TD
-0.0001 Tc
[(outside)-343.4(t)0.3(he)-343.4(closed)-343.4(unit)-343.9(d)-0.1(isc.)-473(Since)-343.4(the)-343.4(s)-0.4(et)-342(of)-343.2(Pisot)-343.9(n)27.9(um-)]TJ
0 -1.3 TD
-0.0002 Tc
[(b)-28.2(e)-0.2(rs)-494.7(is)-496.5(closed)-496.2([Salem)-496.6(44],)-537.3(this)-496.5(n)27.8(u)-0.2(m)28.2(b)-28.2(er,)]TJ
/F6 1 Tf
18.299 0 TD
0 Tc
()Tj
/F15 1 Tf
6.9738 0 0 6.9738 490.905 444.297 Tm
()Tj
/F14 1 Tf
1.1383 0 TD
(,)Tj
/F15 1 Tf
0.3394 0 TD
()Tj
/F14 1 Tf
1.1383 0 TD
0.0001 Tc
(,m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 518.589 443.298 Tm
0 Tc
(3)Tj
/F14 1 Tf
6.9738 0 0 6.9738 522.477 444.297 Tm
0.0001 Tc
(,...,m)Tj
/F21 1 Tf
4.9813 0 0 4.9813 541.386 443.244 Tm
0 Tc
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 546.237 445.791 Tm
(,)Tj
-24.3225 -1.3 TD
[(m)28.4(u)0(st)-333.8(b)-28(e)-332.5(a)-333.8(P)0.3(isot)-333.8(n)28(u)0(m)28.4(b)-28(er.)]TJ
1.1997 -1.3 TD
-0.0002 Tc
[(Similarly)83.1(,)-450.5(w)28.2(e)-425.7(l)0.2(et)-426.2(the)-425.7(r)-0.6(emaining)]TJ
/F6 1 Tf
14.2383 0 TD
0 Tc
(m)Tj
/F14 1 Tf
6.9738 0 0 6.9738 466.47 418.3951 Tm
(i)Tj
/F12 1 Tf
9.9626 0 0 9.9626 474.075 419.889 Tm
0.431 Tc
()Tj
/F2 1 Tf
2.431 0 TD
0.0001 Tc
[(,)-447.5(p)0.1(ro)-27.5(ducing)]TJ
-19.5102 -1.3 TD
-0.0002 Tc
[(a)-413.5(P)0.1(isot)-415.3(n)27.8(u)-0.2(m)28.2(b)-28.2(er)]TJ
/F6 1 Tf
7.2912 0 TD
0 Tc
()Tj
/F2 1 Tf
0.9097 0 TD
(=)Tj
/F6 1 Tf
1.1898 0 TD
()Tj
/F15 1 Tf
6.9738 0 0 6.9738 402.156 405.444 Tm
()Tj
/F14 1 Tf
1.1383 0 TD
-0.0002 Tc
(,...,)Tj
/F15 1 Tf
1.6958 0 TD
0 Tc
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 434.4839 406.938 Tm
-0.0002 Tc
[(that)-415.3(is)-414.3(the)-414.9(unique)-414(r)-0.6(o)-27.8(o)0.2(t)-414.4(o)0.2(f)]TJ
/F6 1 Tf
-13.1053 -1.3 TD
0 Tc
(P)Tj
/F13 1 Tf
6.9738 0 0 6.9738 310.32 392.187 Tm
0.0001 Tc
(\(1)Tj
/F14 1 Tf
1.0157 0 TD
0 Tc
(,)Tj
/F13 1 Tf
0.3394 0 TD
(1)Tj
/F14 1 Tf
0.5691 0 TD
-0.0002 Tc
(,...,)Tj
/F13 1 Tf
1.6958 0 TD
-0.0003 Tc
(1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 347.346 393.987 Tm
-0.0001 Tc
[(outside)-422(t)0.3(he)-422(closed)-422(unit)-421.5(d)-0.1(isc.)-708.8(Hence)]TJ
/F6 1 Tf
16.3034 0 TD
0 Tc
(P)Tj
/F13 1 Tf
6.9738 0 0 6.9738 516.168 392.187 Tm
0.0001 Tc
(\(1)Tj
/F14 1 Tf
1.0157 0 TD
0 Tc
(,)Tj
/F13 1 Tf
0.3394 0 TD
(1)Tj
/F14 1 Tf
0.5691 0 TD
0.0001 Tc
(,...,)Tj
/F13 1 Tf
1.6971 0 TD
-0.0003 Tc
(1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 303.921 381.036 Tm
0 Tc
[(has)-333.7(t)0.4(he)-333.4(desired)-333.4(form.)]TJ
1.1997 -1.3 TD
-0.0002 Tc
[(Finally)83.1(,)-305.1(w)28.2(e)-296.5(n)-0.2(ote)-296.5(that)-297(in)-296.5(whatev)28(e)-0.2(r)-297.8(manner)-296.9(the)]TJ
/F6 1 Tf
19.9495 0 TD
0 Tc
(m)Tj
/F14 1 Tf
6.9738 0 0 6.9738 523.368 366.5911 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 529.632 368.0851 Tm
-0.0001 Tc
(tend)Tj
-22.6557 -1.3 TD
-0.0002 Tc
[(to)-504.8(innit)28.2(y)83.1(,)]TJ
/F6 1 Tf
5.2451 0 TD
0 Tc
(P)Tj
/F13 1 Tf
6.9738 0 0 6.9738 362.574 353.334 Tm
0.0001 Tc
(\(1)Tj
/F14 1 Tf
1.0157 0 TD
0 Tc
(,)Tj
/F13 1 Tf
0.3394 0 TD
(1)Tj
/F14 1 Tf
0.5691 0 TD
0.0001 Tc
(,...,)Tj
/F13 1 Tf
1.6971 0 TD
-0.0003 Tc
(1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 400.428 355.134 Tm
-0.0002 Tc
[(ev)28(en)27.8(tually)-506.8(dominates)-506.4(o)0.2(utside)-506.1(the)]TJ
-9.6869 -1.3 TD
-0.0001 Tc
[(unit)-445.9(c)-0.1(ircle,)-474.8(and)-446.4(a)-445.9(Rouc)27.9(h)27.9()]TJ
11.0213 0 TD
[(e)-447.3(a)0.3(rgumen)27.9(t)-447.7(near)]TJ
/F6 1 Tf
7.817 0 TD
0 Tc
()Tj
/F2 1 Tf
0.9431 0 TD
[(sho)28.4(w)0.4(s)-447.5(t)0.4(hat)]TJ
-19.7814 -1.3 TD
-0.0001 Tc
[(the)-333.5(S)-0.1(alem)-334.8(n)27.9(um)28.3(b)-28.1(e)-0.1(rs)-332.9(con)27.9(v)28.1(erge)-335.3(to)]TJ
/F6 1 Tf
14.0115 0 TD
0 Tc
()Tj
/F2 1 Tf
0.4978 0 TD
(.)Tj
ET
542.223 335.807 m
549 335.807 l
542.425 329.628 m
542.425 335.613 l
548.806 329.628 m
548.806 335.613 l
542.223 329.435 m
549 329.435 l
S
BT
/F3 1 Tf
9.9626 0 0 9.9626 303.921 310.0261 Tm
-0.0002 Tc
[(Lemma)-348.5(4.5.)]TJ
/F11 1 Tf
5.7338 0 TD
-0.0518 Tc
[(Le)-51.6(t)]TJ
/F6 1 Tf
1.7905 0 TD
0 Tc
(G)Tj
/F11 1 Tf
1.2069 0 TD
0.0002 Tc
[(b)51.9(e)-422.4(a)-421(g)0.4(r)51.5(aph)-421(with)-421(two)-421(\()-0.1(p)51.5(e)0.4(rhaps)-420.2(e)51.9(q)0.4(ual\))]TJ
-8.7312 -1.3 TD
0 Tc
[(distinguishe)51.7(d)-519.6(vertic)51.7(e)0.2(s)]TJ
/F6 1 Tf
9.8668 0 TD
(v)Tj
/F13 1 Tf
6.9738 0 0 6.9738 407.052 295.5811 Tm
(1)Tj
/F11 1 Tf
9.9626 0 0 9.9626 416.682 297.075 Tm
-0.0001 Tc
(and)Tj
/F6 1 Tf
2.1031 0 TD
0 Tc
(v)Tj
/F13 1 Tf
6.9738 0 0 6.9738 442.467 295.5811 Tm
(2)Tj
/F11 1 Tf
9.9626 0 0 9.9626 446.94 297.075 Tm
0.9427 Tc
[(.L)994.5(e)942.9(t)]TJ
/F6 1 Tf
3.1365 0 TD
0 Tc
(G)Tj
/F13 1 Tf
6.9738 0 0 6.9738 486.018 300.684 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 496.206 299.6851 Tm
(1)Tj
/F14 1 Tf
6.9738 0 0 6.9738 500.085 300.684 Tm
0.0001 Tc
(,m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 509.526 299.6851 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 513.4139 300.684 Tm
(\))Tj
/F11 1 Tf
9.9626 0 0 9.9626 522.189 297.075 Tm
0.0002 Tc
[(b)51.9(e)-519.1(the)]TJ
-21.9087 -1.3 TD
-0.0001 Tc
[(gr)51.2(aph)-497.2(obtaine)51.6(d)-498.1(b)0.1(y)-497.4(i)0.3(dentifying)-499.5(the)-496.8(endvertic)51.6(e)0.1(s)-498.2(o)-0.3(f)-497.4(a)-497.2(new)]TJ
/F2 1 Tf
T*
0 Tc
(\()Tj
/F6 1 Tf
0.3885 0 TD
(m)Tj
/F13 1 Tf
6.9738 0 0 6.9738 316.539 269.679 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 324.027 271.173 Tm
(+)Tj
/F6 1 Tf
1.0804 0 TD
(m)Tj
/F13 1 Tf
6.9738 0 0 6.9738 343.539 269.679 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 351.018 271.173 Tm
0.3027 Tc
[(+3)303.1(\))]TJ
/F11 1 Tf
1.9685 0 TD
0 Tc
[(-vertex)-469.3(p)51.3(ath)-469.1(with)-468.2(vertic)51.7(e)0.2(s)]TJ
/F6 1 Tf
11.7178 0 TD
(v)Tj
/F13 1 Tf
6.9738 0 0 6.9738 492.201 269.679 Tm
(1)Tj
/F11 1 Tf
9.9626 0 0 9.9626 501.336 271.173 Tm
-0.0001 Tc
(and)Tj
/F6 1 Tf
2.0534 0 TD
0 Tc
(v)Tj
/F13 1 Tf
6.9738 0 0 6.9738 526.626 269.679 Tm
(2)Tj
/F11 1 Tf
9.9626 0 0 9.9626 535.761 271.173 Tm
0.0004 Tc
(\(so)Tj
-23.2709 -1.3009 TD
0.0002 Tc
(that)Tj
/F6 1 Tf
2.1094 0 TD
0 Tc
(G)Tj
/F13 1 Tf
6.9738 0 0 6.9738 332.766 261.8311 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 342.954 260.832 Tm
(1)Tj
/F14 1 Tf
6.9738 0 0 6.9738 346.842 261.8311 Tm
0.0001 Tc
(,m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 356.283 260.832 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 360.162 261.8311 Tm
(\))Tj
/F11 1 Tf
9.9626 0 0 9.9626 367.992 258.213 Tm
0.0002 Tc
(has)Tj
/F6 1 Tf
1.8537 0 TD
0 Tc
(m)Tj
/F13 1 Tf
6.9738 0 0 6.9738 395.208 256.7191 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 402.363 258.213 Tm
(+)Tj
/F6 1 Tf
1.047 0 TD
(m)Tj
/F13 1 Tf
6.9738 0 0 6.9738 421.542 256.7191 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 428.697 258.213 Tm
0.2692 Tc
(+1)Tj
/F11 1 Tf
1.9703 0 TD
0 Tc
[(mor)51.3(e)-423.5(vertic)51.7(e)0.2(s)-424(than)]TJ
/F6 1 Tf
8.6038 0 TD
(G)Tj
/F11 1 Tf
0.7859 0 TD
0.0004 Tc
(\).)Tj
-23.8845 -1.3 TD
-0.0518 Tc
[(Le)-51.6(t)]TJ
/F6 1 Tf
1.7264 0 TD
0 Tc
(R)Tj
/F13 1 Tf
6.9738 0 0 6.9738 328.77 248.88 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 338.958 247.881 Tm
(1)Tj
/F14 1 Tf
6.9738 0 0 6.9738 342.828 248.88 Tm
0.0001 Tc
(,m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 352.269 247.881 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 356.148 248.88 Tm
(\))Tj
/F11 1 Tf
9.9626 0 0 9.9626 363.33 245.2621 Tm
[(b)51.7(e)-358.5(the)-356.7(r)51.3(e)51.7(cipr)51.3(o)51.3(c)51.7(al)-359.7(p)51.3(o)-0.2(lynomial)-358.7(of)]TJ
/F6 1 Tf
13.5192 0 TD
(G)Tj
/F13 1 Tf
6.9738 0 0 6.9738 505.845 248.88 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 516.033 247.881 Tm
(1)Tj
/F14 1 Tf
6.9738 0 0 6.9738 519.912 248.88 Tm
0.0001 Tc
(,m)Tj
/F22 1 Tf
4.9813 0 0 4.9813 529.353 247.881 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 533.241 248.88 Tm
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[(Applying)-334.9(Lemma)-334(4.2)-334.9(for)-333.9(t)0.2(he)-334.5(case)]TJ
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[(=2)278.7(,)-55.5(w)306.7(e)-55.1(g)278.7(e)278.3(t)]TJ
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9.9626 0 0 9.9626 235.647 508.602 Tm
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[(+1)222.7(\))]TJ
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[(Comparing)-335.9(with)]TJ
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[(w)28.3(e)-334.4(get)-333.9(t)0.3(he)-333.5(adv)28.1(e)-0.1(rtised)-334.4(result.)]TJ
ET
0 0 0 1 K
0 J 0 j 0.405 w 10 M []0 d
1 i
301.302 406.808 m
308.079 406.808 l
301.504 400.629 m
301.504 406.614 l
307.885 400.629 m
307.885 406.614 l
301.302 400.436 m
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S
BT
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[(5.)-1201(PROOF)-278.9(OF)-278(THEOREM)-280.2(1)0.2(.1)]TJ
/F2 1 Tf
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[(Consider)-329.4(an)-329.1(innite)-329.1(sequence)-328.1(of)-328.8(non)27.8(t)0.2(rivial)-330.4(Salem)-329.5(g)0.2(raphs)]TJ
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(G)Tj
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[(,)-455(f)0.1(or)-431.4(whic)27.9(h)-431(t)0.3(he)-431(Salem)-431.5(n)27.9(um)28.3(b)-28.1(e)-0.1(rs)]TJ
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[(\))-430.8(t)0.1(end)-431.2(to)-431.7(a)-429.9(limit.)]TJ
-16.8228 -1.3 TD
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[(W)82.6(e)-335.4(are)-336.3(i)0.2(n)27.8(t)0.2(erested)-337.2(i)0.2(n)-336.3(limit)-337.6(p)-28.2(oin)27.8(ts)-337.5(of)-336(the)-336.3(s)-0.5(et)]TJ
/F6 1 Tf
18.9892 0 TD
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(T)Tj
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(graph)Tj
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9.9626 0 0 9.9626 278.361 312.285 Tm
0.3361 Tc
[(,s)335.8(ow)364.5(e)]TJ
-21.6169 -1.3 TD
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T*
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T*
[(supp)-28.1(ose)-457.2(t)0.3(hat)-459.5(t)0.3(he)-458.1(graphs)-458.4(are)-458.1(e)-0.1(ither)-459.4(all)-458.6(bipartite,)-491.1(o)0.3(r)-458.5(all)]TJ
T*
[(non)27.9(b)-0.1(ipartite.)-612.1(I)-0.3(ndeed)-387.7(w)28.3(e)-389.5(shall)-389(supp)-28.1(ose)-387.7(t)0.3(hat)-389(t)0.3(hey)-389.3(are)-388.6(all)]TJ
T*
-0.0002 Tc
[(non)27.8(b)-0.2(ipartite,)-412.6(a)0.2(nd)-395.9(lea)28.2(v)28(e)-396.8(t)0.2(he)-395.9(trivial)-396.3(mo)-27.8(dications)-398(f)0(or)-396.3(the)]TJ
T*
-0.0001 Tc
[(bipartite)-411.2(case)-410.3(to)-410.7(the)-410.3(r)-0.5(eader.)-672.7(T)0.3(hese)-410.3(S)-0.1(alem)-410.7(n)27.9(um)28.3(b)-28.1(e)-0.1(rs)-409.7(are)]TJ
T*
[(b)-28.1(o)0.3(unded)-505.1(ab)-28.1(o)28.3(v)28.1(e,)-548(and)-505.1(hence)-505.1(so)-503.8(are)-505.1(t)0.3(he)-505.1(indices)-505.4(of)-504.9(their)]TJ
0 -1.3009 TD
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[(graphs.)-439.7(H)0(ence,)-322.3(Prop)-28.2(osition)-320(3.2)-319.6(giv)28(es)-320.3(an)-319.1(upp)-28.2(er)-318.6(b)-28.2(o)0.2(und)-319.1(on)]TJ
0 -1.3 TD
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[(the)-368.7(n)27.9(um)28.3(b)-28.1(e)-0.1(r)-369.1(o)0.3(f)-369.4(v)28.1(ertices)-369(of)-369.4(degree)-368.7(n)-0.1(ot)-368.2(equal)-369.1(t)0.3(o)-369.2(2)-369.2(o)0.3(f)-368.5(t)0.3(hese)]TJ
T*
-0.0002 Tc
[(Salem)-353.9(g)0.2(raphs,)-358.4(a)0.2(nd)-353.4(Lemma)-353(2.4)-353.9(giv)28(es)-354.7(an)-353.4(upp)-28.2(er)-352.9(b)-28.2(o)0.2(und)-353.4(on)]TJ
T*
-0.0001 Tc
[(the)-447.3(degrees)-446.7(of)-447.1(v)28.1(e)-0.1(rtices)-447.6(that)-447.7(eac)27.9(h)-447.3(suc)27.9(h)-446.4(graph)-447.3(c)-0.1(an)-447.3(ha)28.3(v)28.1(e)-0.1(.)]TJ
T*
-0.0003 Tc
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/F6 1 Tf
19.7814 0 TD
0 Tc
(B)Tj
/F13 1 Tf
6.9738 0 0 6.9738 267.633 155.3701 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 275.346 156.864 Tm
-0.0001 Tc
[(v)28.1(e)-0.1(rtices)]TJ
-21.3142 -1.3 TD
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/F6 1 Tf
16.0739 0 TD
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(B)Tj
/F13 1 Tf
6.9738 0 0 6.9738 230.697 142.419 Tm
(2)Tj
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9.9626 0 0 9.9626 239.598 143.9131 Tm
-0.0001 Tc
[(is)-444.9(nite.)-780.2(T)0.3(h)27.9(u)-0.1(s,)]TJ
-17.726 -1.3 TD
-0.0002 Tc
[(up)-28.2(on)-330(asso)-27.8(ciating)-331.3(e)-0.2(ac)27.8(h)-330(S)-0.2(alem)-331.3(g)0.2(raph)-330(in)-330(the)-330(s)-0.5(equence)-330(with)]TJ
T*
[(the)-367.9(m)28.2(ultigraph)-370.6(with)-368.8(no)-368.4(v)28(e)-0.2(rtices)-368.2(of)-368.6(degree)-367.9(2)-367.4(ha)28.2(ving)-369.3(that)]TJ
T*
-0.0001 Tc
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T*
-0.0002 Tc
[(tices)-358.3(of)-356.8(degree)-357.1(2)-357.5(along)-357.5(edges)-357.4(of)-357.7(the)-357.1(m)28.2(ultigraph)-359.8(r)-0.6(etriev)28(es)]TJ
T*
[(the)-328.1(S)-0.2(alem)-328.6(g)0.2(raph\),)-330.4(w)28.2(e)-328.1(o)0.2(btain)-330(only)-327.9(nitely)-329.7(man)27.8(y)-328.8(d)-0.2(ieren)27.8(t)]TJ
26.4002 63.8 TD
-0.0001 Tc
[(m)28.3(u)-0.1(ltigraphs.)-491.1(H)0.1(ence,)-352.9(b)27.9(y)-348.6(replacing)-349.3(t)0.3(he)-348.8(sequence)-347.9(of)-349.5(Salem)]TJ
0 -1.3 TD
0 Tc
[(graphs)-480.9(b)28(y)-480.4(a)-480.2(s)-0.3(ubsequence,)-516.3(if)-481.3(necessary)83.3(,)-516.3(w)28.4(e)-481.5(c)0(an)-480.6(assume)]TJ
T*
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(6)Tj
/F15 1 Tf
6.9738 0 0 6.9738 420.327 565.887 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 430.65 567.876 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 434.529 565.887 Tm
0.0006 Tc
(+1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 474.435 569.316 Tm
0.1658 Tc
(, )Tj
/F2 1 Tf
1.2801 0 TD
0.2783 Tc
(=6)Tj
/F6 1 Tf
-36.9625 -3.3 TD
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 126.297 534.9451 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 130.77 536.439 Tm
-0.0004 Tc
(\(3\))Tj
/F1 1 Tf
2.3135 -0.4996 TD
2.4992 Tc
()Tj
ET
153.819 531.467 m
228.546 531.467 l
S
BT
9.9626 0 0 9.9626 168.7592 531.462 Tm
0.9996 Tc
()Tj
ET
183.703 531.462 m
183.703 546.411 l
S
BT
9.9626 0 0 9.9626 183.699 546.402 Tm
0 Tc
()Tj
1.5005 -1.4996 TD
1.0001 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 120.141 515.622 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 125.829 514.623 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 129.717 515.622 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 135.405 514.623 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 139.293 515.622 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 144.981 514.623 Tm
(4)Tj
ET
120.141 514.034 m
148.869 514.034 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 128.025 508.098 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 133.713 507.099 Tm
0.0006 Tc
(18)Tj
/F2 1 Tf
9.9626 0 0 9.9626 152.829 511.536 Tm
0 Tc
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 164.538 516.369 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 192.159 519.375 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 196.038 516.369 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 226.665 519.375 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 230.544 516.369 Tm
0.0002 Tc
(+1\))Tj
ET
164.538 514.034 m
243.747 514.034 l
S
BT
/F14 1 Tf
6.9738 0 0 6.9738 188.01 508.098 Tm
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 192.105 510.096 Tm
(6)Tj
/F15 1 Tf
6.9738 0 0 6.9738 195.984 508.098 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 206.307 510.096 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 210.195 508.098 Tm
0.0006 Tc
(+1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 244.944 511.536 Tm
0.1658 Tc
(, )Tj
/F2 1 Tf
1.2792 0 TD
0.2783 Tc
[(=1)278.7(2)]TJ
/F6 1 Tf
8.0735 2.4996 TD
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 345.474 534.9451 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 349.947 536.439 Tm
-0.0004 Tc
(\(4\))Tj
/F1 1 Tf
2.3135 -0.4996 TD
0 Tc
()Tj
ET
372.996 531.467 m
447.723 531.467 l
S
BT
9.9626 0 0 9.9626 387.936 531.462 Tm
2.5001 Tc
()Tj
1.5005 0 TD
0 Tc
()Tj
ET
402.88 531.462 m
402.88 546.411 l
S
BT
9.9626 0 0 9.9626 402.885 546.402 Tm
()Tj
1.4996 -1.4996 TD
1.0001 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 341.019 515.622 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 346.707 514.623 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 350.586 515.622 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 356.274 514.623 Tm
(5)Tj
ET
339.318 514.034 m
361.863 514.034 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 339.318 508.098 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 345.006 507.099 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 348.894 508.098 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 354.582 507.099 Tm
0.0006 Tc
(18)Tj
/F2 1 Tf
9.9626 0 0 9.9626 365.823 511.536 Tm
0 Tc
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 377.532 516.369 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 384.741 519.375 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 388.629 516.369 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 419.256 519.375 Tm
(4)Tj
/F13 1 Tf
6.9738 0 0 6.9738 423.135 516.369 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 433.35 519.375 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 437.229 516.369 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 447.444 519.375 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 451.323 516.369 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0002 Tc
(+1\))Tj
ET
377.532 514.034 m
474.732 514.034 l
S
BT
6.9738 0 0 6.9738 396.684 508.098 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 424.305 510.096 Tm
(6)Tj
/F15 1 Tf
6.9738 0 0 6.9738 428.184 508.098 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 438.507 510.096 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 442.386 508.098 Tm
0.0002 Tc
(+1\))Tj
/F6 1 Tf
9.9626 0 0 9.9626 475.929 511.536 Tm
0.1658 Tc
(, )Tj
/F2 1 Tf
1.2801 0 TD
0 Tc
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 500.391 515.46 Tm
-0.0003 Tc
(15)Tj
ET
500.391 514.034 m
508.338 514.034 l
S
BT
6.9738 0 0 6.9738 502.38 508.098 Tm
0 Tc
(2)Tj
/F6 1 Tf
9.9626 0 0 9.9626 118.944 478.659 Tm
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 126.297 477.165 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 130.77 478.659 Tm
-0.0004 Tc
(\(5\))Tj
/F1 1 Tf
2.3135 -0.4996 TD
5.4993 Tc
()Tj
ET
153.819 473.678 m
228.546 473.678 l
S
BT
9.9626 0 0 9.9626 168.7592 473.682 Tm
0.9996 Tc
()Tj
ET
183.703 473.682 m
183.703 488.631 l
S
BT
9.9626 0 0 9.9626 183.699 488.622 Tm
0 Tc
()Tj
1.5005 -1.4996 TD
1.0001 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 120.141 457.842 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 125.829 456.843 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 129.717 457.842 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 135.405 456.843 Tm
(8)Tj
ET
120.141 456.254 m
139.293 456.254 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 123.237 450.318 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 128.925 449.319 Tm
0.0006 Tc
(18)Tj
/F2 1 Tf
9.9626 0 0 9.9626 143.253 453.756 Tm
0 Tc
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 154.971 458.5891 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 182.592 461.595 Tm
(4)Tj
/F13 1 Tf
6.9738 0 0 6.9738 186.471 458.5891 Tm
0.0002 Tc
(+1\))Tj
ET
154.971 456.245 m
199.674 456.245 l
S
BT
/F14 1 Tf
6.9738 0 0 6.9738 161.181 450.318 Tm
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 165.276 452.307 Tm
(6)Tj
/F15 1 Tf
6.9738 0 0 6.9738 169.164 450.318 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 179.487 452.307 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 183.366 450.318 Tm
0.0006 Tc
(+1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 200.862 453.756 Tm
0.1658 Tc
(, )Tj
/F2 1 Tf
1.2801 0 TD
0.2774 Tc
(=4)Tj
/F6 1 Tf
12.4973 2.4996 TD
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 345.474 477.165 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 349.947 478.659 Tm
-0.0004 Tc
(\(6\))Tj
/F1 1 Tf
2.3135 -0.4996 TD
0 Tc
()Tj
ET
372.996 473.678 m
447.723 473.678 l
S
BT
9.9626 0 0 9.9626 387.936 473.682 Tm
5.5002 Tc
()Tj
1.5005 0 TD
0 Tc
()Tj
ET
402.88 473.682 m
402.88 488.631 l
S
BT
9.9626 0 0 9.9626 402.885 488.622 Tm
()Tj
1.4996 -1.4996 TD
1.0001 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 339.318 457.842 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 345.006 456.843 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 348.894 457.842 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 354.582 456.843 Tm
0.0006 Tc
(12)Tj
ET
339.318 456.254 m
361.863 456.254 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 339.318 450.318 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 345.006 449.319 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 348.894 450.318 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 354.582 449.319 Tm
0.0006 Tc
(18)Tj
/F2 1 Tf
9.9626 0 0 9.9626 365.823 453.756 Tm
0 Tc
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 377.532 458.5891 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 384.741 461.595 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 388.629 458.5891 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 419.256 461.595 Tm
(4)Tj
/F15 1 Tf
6.9738 0 0 6.9738 423.135 458.5891 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 433.458 461.595 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 437.337 458.5891 Tm
0.0002 Tc
(+1\))Tj
ET
377.532 456.245 m
450.54 456.245 l
S
BT
6.9738 0 0 6.9738 384.579 450.318 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 412.2 452.307 Tm
(6)Tj
/F15 1 Tf
6.9738 0 0 6.9738 416.079 450.318 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 426.402 452.307 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 430.29 450.318 Tm
0.0002 Tc
(+1\))Tj
/F6 1 Tf
9.9626 0 0 9.9626 451.737 453.756 Tm
0.1658 Tc
(, )Tj
/F2 1 Tf
1.2801 0 TD
0 Tc
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 476.199 457.6801 Tm
(3)Tj
ET
476.199 456.254 m
480.177 456.254 l
S
BT
6.9738 0 0 6.9738 476.199 450.318 Tm
(2)Tj
/F6 1 Tf
9.9626 0 0 9.9626 118.944 420.879 Tm
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 126.297 419.385 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 130.77 420.879 Tm
-0.0004 Tc
(\(7\))Tj
/F1 1 Tf
2.3135 -0.5005 TD
0 Tc
()Tj
2.9992 1.5005 TD
()Tj
ET
153.819 415.898 m
228.546 415.898 l
S
BT
9.9626 0 0 9.9626 168.759 415.893 Tm
0.9996 Tc
()Tj
ET
183.703 415.893 m
183.703 430.842 l
S
BT
9.9626 0 0 9.9626 183.699 430.842 Tm
0 Tc
()Tj
1.5005 -1.5005 TD
1.0001 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 126.621 400.053 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 132.309 399.054 Tm
(7)Tj
ET
120.141 398.465 m
142.686 398.465 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 120.141 392.538 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 125.829 391.539 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 129.717 392.538 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 135.405 391.539 Tm
0.0006 Tc
(18)Tj
/F2 1 Tf
9.9626 0 0 9.9626 146.646 395.967 Tm
0 Tc
(=)Tj
/F14 1 Tf
6.9738 0 0 6.9738 158.355 399.891 Tm
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 162.45 402.897 Tm
(6)Tj
/F13 1 Tf
6.9738 0 0 6.9738 166.338 399.891 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 176.553 402.897 Tm
(5)Tj
/F13 1 Tf
6.9738 0 0 6.9738 180.432 399.891 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 190.647 402.897 Tm
(4)Tj
/F13 1 Tf
6.9738 0 0 6.9738 194.526 399.891 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 204.741 402.897 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 208.629 399.891 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 218.844 402.897 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 222.723 399.891 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0006 Tc
(+1)Tj
ET
158.355 398.465 m
243.018 398.465 l
S
BT
6.9738 0 0 6.9738 171.234 392.538 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 198.855 394.527 Tm
(6)Tj
/F15 1 Tf
6.9738 0 0 6.9738 202.734 392.538 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 213.057 394.527 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 216.945 392.538 Tm
0.0002 Tc
(+1\))Tj
/F6 1 Tf
9.9626 0 0 9.9626 244.215 395.967 Tm
0.1658 Tc
(, )Tj
/F2 1 Tf
1.2801 0 TD
0 Tc
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 268.677 399.891 Tm
(7)Tj
ET
268.677 398.465 m
272.655 398.465 l
S
BT
6.9738 0 0 6.9738 268.677 392.538 Tm
(2)Tj
/F3 1 Tf
8.9664 0 0 8.9664 104.679 368.076 Tm
[(FIGURE)-277.9(2)]TJ
/F9 1 Tf
4.3341 0 TD
[(.)-456.3(T)-0.5(he)-341.8(ro)-28.1(oted)-343.4(trees)-343.4(that)-342.1(are)-341.8(p)-0.1(rop)-28.2(e)0.5(r)-342.8(subsets)-343.4(of)]TJ
20.7416 0.2529 TD
()Tj
/F7 1 Tf
-0.2349 -0.2529 TD
(E)Tj
/F8 1 Tf
5.9776 0 0 5.9776 334.188 367.077 Tm
(6)Tj
/F9 1 Tf
8.9664 0 0 8.9664 341.415 368.076 Tm
0.0001 Tc
(and)Tj
2.2333 0.2529 TD
0 Tc
()Tj
/F7 1 Tf
-0.2349 -0.2529 TD
(E)Tj
/F8 1 Tf
5.9776 0 0 5.9776 366.111 367.077 Tm
(7)Tj
/F9 1 Tf
8.9664 0 0 8.9664 370.26 368.076 Tm
[(,)-342.9(but)-342.1(not)-343.1(subtrees)-342.4(of)-342.4(an)28(y)]TJ
11.7017 0.2529 TD
()Tj
/F7 1 Tf
-0.2389 -0.2529 TD
(D)Tj
/F20 1 Tf
5.9776 0 0 5.9776 480.636 367.077 Tm
(n)Tj
/F9 1 Tf
8.9664 0 0 8.9664 485.739 368.076 Tm
(.)Tj
/F3 1 Tf
9.9626 0 0 9.9626 40.905 342.417 Tm
-0.0001 Tc
[(Remark)-286.9(5.1.)]TJ
/F2 1 Tf
5.657 0 TD
[(Examining)-343.9(t)0.3(he)-342.5(pro)-27.7(o)0.3(f,)-343.8(w)28.3(e)-342.5(see)-341.6(t)0.3(hat)-342(t)0.3(he)-342.5(n)27.9(u)-0.1(m-)]TJ
-5.657 -1.2999 TD
0.028 Tc
[(be)28(r)]TJ
/F6 1 Tf
1.9043 0 TD
0 Tc
(m)Tj
/F2 1 Tf
1.3632 0 TD
-0.0002 Tc
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T*
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ET
222.57 90.773 m
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BT
/F6 1 Tf
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ET
258.084 90.773 m
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BT
/F6 1 Tf
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[(cyclotomic)-265.8(trees,)-276.2(along)-264.5(with)-264(their)-264.4(q)0(uotien)27.8(t)0.2(s)-265.2(a)0.2(nd)]TJ
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T*
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1.1997 -1.3 TD
[(In)-345.2(our)-346.5(list)-346.6(\()0.3(Figures)-345.5(27\),)-351.1(eac)27.9(h)-346.1(en)27.9(try)-345.9(f)0.1(or)-346.5(a)-345.7(t)0.3(ree)]TJ
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[(tains)-232.8(t)0.1(he)-232.5(follo)28.1(wing:)-396.4(a)-232(n)-0.3(ame)-232.5(for)]TJ
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13.2527 0 TD
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[(,)-251.7(b)-0.1(ased)-231.4(on)-232.3(Co)28.3(xeter)-233.6(g)0.3(raph)]TJ
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[(notation;)-265.4(a)-227.4(picture)-227(o)0.2(f)]TJ
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[(,)-248.2(with)-228.8(the)-227.9(r)-0.6(o)-27.8(o)0.2(t)-227.4(c)-0.2(ircled;)-263.5(its)-228.2(quotien)27.8(t)]TJ
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[(\)i)388.4(s)]TJ
-23.1508 -1.3 TD
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[(th)-334.6(cyclotomic)-336.4(p)-28.3(olynomial.)]TJ
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-1.1997 -1.3 TD
[(can)-238.6(b)-28.1(e)-237.7(u)-0.1(sed)-238.6(f)0.1(or)-238.1(constructing)-240(b)-0.1(ipartite)-239.5(Salem)-239.1(g)0.3(raphcs)-238.9(\(but)]TJ
T*
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1.1997 -1.3 TD
[(Note)-345.3(that,)-348.5(since)]TJ
7.5775 0.2529 TD
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(E)Tj
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(E)Tj
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(8)Tj
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[(\(5\))-345(ha)28.1(v)27.9(e)-345.4(the)-344.5(s)-0.6(ame)-344.5(quo-)]TJ
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T*
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T*
[(same)-333.5(Salem)-334.8(n)27.9(um)28.3(b)-28.1(e)-0.1(r.)]TJ
1.1997 -1.3 TD
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[(F)82.5(o)0.2(r)-469.5(e)-0.2(ac)27.8(h)-470(o)0.2(f)-469.7(t)0.2(he)-470(Salem)-470.4(q)0(uotien)27.8(t)0.2(s)]TJ
/F6 1 Tf
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[(\))-468.7(c)-0.3(atalogued)-472.8(in)]TJ
-17.7732 -1.3 TD
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/F6 1 Tf
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()Tj
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[(\)i)283.1(sa)283.1(n)]TJ
-21.9188 -1.3 TD
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[(in)27.8(terlacing)-247.3(q)0(uotien)27.8(t)0.2(,)-265.4(a)0.2(s)-246.3(dened)-245(in)-245.9([McKee)-245.9(and)-245.9(S)-0.2(m)28.2(y)0(th)-246.8(05].)]TJ
T*
-0.0001 Tc
[(This)-374.4(is)-374.4(an)-374.1(easy)-373.9(consequence)-373.2(of)-374.8(the)-374.1(I)-0.3(n)27.9(t)0.3(erlacing)-374.6(T)0.3(heorem)]TJ
0 -1.3009 TD
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[(\(Lemma)-335(2.1\).)]TJ
ET
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S
BT
/F13 1 Tf
6.9738 0 0 6.9738 150.12 551.946 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 155.808 550.947 Tm
0.0006 Tc
(30)Tj
/F2 1 Tf
9.9626 0 0 9.9626 174.924 555.384 Tm
0 Tc
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 189.531 560.217 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 217.152 563.223 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 221.031 560.217 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 251.658 563.223 Tm
(4)Tj
/F13 1 Tf
6.9738 0 0 6.9738 255.537 560.217 Tm
0.0002 Tc
(+1\))Tj
ET
186.633 557.882 m
271.629 557.882 l
S
BT
/F14 1 Tf
6.9738 0 0 6.9738 186.633 551.946 Tm
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 190.728 553.944 Tm
(8)Tj
/F13 1 Tf
6.9738 0 0 6.9738 194.616 551.946 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 204.831 553.944 Tm
(7)Tj
/F15 1 Tf
6.9738 0 0 6.9738 208.71 551.946 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 219.033 553.944 Tm
(5)Tj
/F15 1 Tf
6.9738 0 0 6.9738 222.921 551.946 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 233.244 553.944 Tm
(4)Tj
/F15 1 Tf
6.9738 0 0 6.9738 237.132 551.946 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 247.455 553.944 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 251.334 551.946 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0006 Tc
(+1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 272.826 555.384 Tm
0.1658 Tc
(, )Tj
/F2 1 Tf
1.2801 0 TD
0.2774 Tc
[(=1)277.8(2)]TJ
/F6 1 Tf
7.4917 2.4996 TD
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 367.569 578.793 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 372.042 580.287 Tm
-0.0004 Tc
(\(6\))Tj
/F1 1 Tf
2.3135 -0.4996 TD
0 Tc
()Tj
ET
395.091 575.315 m
484.758 575.315 l
S
BT
9.9626 0 0 9.9626 410.031 575.3101 Tm
5.5002 Tc
()Tj
1.5005 0 TD
0 Tc
()Tj
ET
424.975 575.31 m
424.975 590.259 l
S
BT
9.9626 0 0 9.9626 424.98 590.25 Tm
()Tj
1.4996 -1.4996 TD
0.9998 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 361.413 559.47 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 367.101 558.471 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 370.989 559.47 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 376.677 558.471 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 380.565 559.47 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 386.253 558.471 Tm
0.0006 Tc
(12)Tj
ET
361.413 557.882 m
393.534 557.882 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 370.989 551.946 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 376.677 550.947 Tm
0.0006 Tc
(30)Tj
/F2 1 Tf
9.9626 0 0 9.9626 397.494 555.384 Tm
0 Tc
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 409.203 560.217 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 436.824 563.223 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 440.703 560.217 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 471.33 563.223 Tm
(4)Tj
/F15 1 Tf
6.9738 0 0 6.9738 475.209 560.217 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 485.532 563.223 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 489.411 560.217 Tm
0.0002 Tc
(+1\))Tj
ET
409.203 557.882 m
502.614 557.882 l
S
BT
/F14 1 Tf
6.9738 0 0 6.9738 413.415 551.946 Tm
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 417.51 553.944 Tm
(8)Tj
/F13 1 Tf
6.9738 0 0 6.9738 421.389 551.946 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 431.604 553.944 Tm
(7)Tj
/F15 1 Tf
6.9738 0 0 6.9738 435.492 551.946 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 445.815 553.944 Tm
(5)Tj
/F15 1 Tf
6.9738 0 0 6.9738 449.694 551.946 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 460.017 553.944 Tm
(4)Tj
/F15 1 Tf
6.9738 0 0 6.9738 463.905 551.946 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 474.228 553.944 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 478.116 551.946 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0006 Tc
(+1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 503.811 555.384 Tm
0.1658 Tc
(, )Tj
/F2 1 Tf
1.2801 0 TD
0.2774 Tc
(=6)Tj
/F6 1 Tf
-37.5262 -3.3 TD
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 150.057 521.0131 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 154.521 522.507 Tm
-0.0004 Tc
(\(7\))Tj
/F1 1 Tf
2.3135 -0.4996 TD
8.5003 Tc
()Tj
ET
177.57 517.526 m
267.237 517.526 l
S
BT
9.9626 0 0 9.9626 192.5102 517.53 Tm
1.0005 Tc
()Tj
ET
207.463 517.53 m
207.463 532.479 l
S
BT
9.9626 0 0 9.9626 207.459 532.47 Tm
0 Tc
()Tj
1.4996 -1.4996 TD
1.0003 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 143.901 501.681 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 149.589 500.682 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 153.468 501.681 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 159.156 500.682 Tm
0.0006 Tc
(18)Tj
ET
143.901 500.093 m
166.446 500.093 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 148.68 494.166 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 154.368 493.167 Tm
0.0006 Tc
(30)Tj
/F2 1 Tf
9.9626 0 0 9.9626 170.397 497.604 Tm
0 Tc
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 195.156 502.428 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 222.777 505.4431 Tm
(6)Tj
/F15 1 Tf
6.9738 0 0 6.9738 226.656 502.428 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 236.979 505.4431 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 240.858 502.428 Tm
0.0002 Tc
(+1\))Tj
ET
182.115 500.093 m
267.111 500.093 l
S
BT
/F14 1 Tf
6.9738 0 0 6.9738 182.115 494.166 Tm
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 186.21 496.155 Tm
(8)Tj
/F13 1 Tf
6.9738 0 0 6.9738 190.089 494.166 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 200.304 496.155 Tm
(7)Tj
/F15 1 Tf
6.9738 0 0 6.9738 204.192 494.166 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 214.515 496.155 Tm
(5)Tj
/F15 1 Tf
6.9738 0 0 6.9738 218.394 494.166 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 228.717 496.155 Tm
(4)Tj
/F15 1 Tf
6.9738 0 0 6.9738 232.605 494.166 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 242.928 496.155 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 246.807 494.166 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0006 Tc
(+1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 268.299 497.604 Tm
0.1658 Tc
(, )Tj
/F2 1 Tf
1.2801 0 TD
0.2774 Tc
(=2)Tj
/F6 1 Tf
8.1132 2.4996 TD
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 369.234 521.0131 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 373.707 522.507 Tm
-0.0004 Tc
(\(8\))Tj
/F1 1 Tf
2.3126 -0.4996 TD
0 Tc
()Tj
ET
396.747 517.526 m
486.414 517.526 l
S
BT
9.9626 0 0 9.9626 411.696 517.53 Tm
()Tj
1.4996 1.4996 TD
()Tj
0 -1.4996 TD
()Tj
ET
426.641 517.53 m
426.641 532.479 l
S
BT
9.9626 0 0 9.9626 426.636 532.47 Tm
()Tj
1.4996 -1.4996 TD
1.0003 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 363.078 501.681 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 368.766 500.682 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 372.654 501.681 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 378.342 500.682 Tm
(4)Tj
/F13 1 Tf
6.9738 0 0 6.9738 382.221 501.681 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 387.909 500.682 Tm
(8)Tj
ET
363.078 500.093 m
391.806 500.093 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 370.953 494.166 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 376.641 493.167 Tm
0.0006 Tc
(30)Tj
/F2 1 Tf
9.9626 0 0 9.9626 395.766 497.604 Tm
0 Tc
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 415.476 502.428 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 443.097 505.4431 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 446.976 502.428 Tm
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 467.388 505.4431 Tm
(4)Tj
/F13 1 Tf
6.9738 0 0 6.9738 471.267 502.428 Tm
0.0002 Tc
(+1\))Tj
ET
407.475 500.093 m
492.471 500.093 l
S
BT
/F14 1 Tf
6.9738 0 0 6.9738 407.475 494.166 Tm
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 411.57 496.155 Tm
(8)Tj
/F13 1 Tf
6.9738 0 0 6.9738 415.458 494.166 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 425.673 496.155 Tm
(7)Tj
/F15 1 Tf
6.9738 0 0 6.9738 429.552 494.166 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 439.875 496.155 Tm
(5)Tj
/F15 1 Tf
6.9738 0 0 6.9738 443.763 494.166 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 454.086 496.155 Tm
(4)Tj
/F15 1 Tf
6.9738 0 0 6.9738 457.965 494.166 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 468.288 496.155 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 472.176 494.166 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0006 Tc
(+1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 493.668 497.604 Tm
0.1658 Tc
(, )Tj
/F2 1 Tf
1.2792 0 TD
0.2783 Tc
(=8)Tj
/F3 1 Tf
8.9664 0 0 8.9664 142.731 463.728 Tm
0 Tc
[(FIGURE)-277.9(3)]TJ
/F9 1 Tf
4.3341 0 TD
[(.)-456.3(T)-0.5(he)-342.8(ro)-28.1(oted)-342.4(trees)-343.4(that)-343.1(are)-341.8(p)-0.1(rop)-28.2(e)0.5(r)-342.8(subsets)-342.4(of)]TJ
20.7426 0.2529 TD
()Tj
/F7 1 Tf
-0.2359 -0.2529 TD
(E)Tj
/F8 1 Tf
5.9776 0 0 5.9776 372.24 462.729 Tm
(8)Tj
/F9 1 Tf
8.9664 0 0 8.9664 376.398 463.728 Tm
[(,)-342.9(but)-342.1(not)-342.1(subtrees)-343.4(of)-342.4(an)28(y)]TJ
11.7007 0.2529 TD
()Tj
/F7 1 Tf
-0.2379 -0.2529 TD
(D)Tj
/F20 1 Tf
5.9776 0 0 5.9776 486.774 462.729 Tm
(n)Tj
/F9 1 Tf
8.9664 0 0 8.9664 491.877 463.728 Tm
(.)Tj
/F2 1 Tf
9.9626 0 0 9.9626 143.343 403.752 Tm
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 148.392 399.738 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 152.865 401.232 Tm
-0.0004 Tc
(\(1\))Tj
/F1 1 Tf
2.3135 -0.4996 TD
0 Tc
()Tj
0 0 TD
()Tj
ET
175.914 396.26 m
235.692 396.26 l
S
BT
9.9626 0 0 9.9626 190.8542 396.255 Tm
0.9996 Tc
()Tj
ET
205.798 396.255 m
205.798 426.144 l
S
BT
9.9626 0 0 9.9626 205.794 411.195 Tm
0 Tc
()Tj
0 1.5005 TD
()Tj
1.5005 -3.0001 TD
0.9996 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 150.12 380.415 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 155.808 379.416 Tm
0.0006 Tc
(12)Tj
ET
142.236 378.827 m
170.964 378.827 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 142.236 372.612 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 147.924 375.015 Tm
(2)Tj
0 -0.9178 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 151.812 372.612 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 157.5 371.613 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 161.388 372.612 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 167.076 371.613 Tm
(3)Tj
/F2 1 Tf
9.9626 0 0 9.9626 174.924 376.329 Tm
(=)Tj
/F14 1 Tf
6.9738 0 0 6.9738 210.159 380.253 Tm
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 214.254 383.259 Tm
(4)Tj
/F15 1 Tf
6.9738 0 0 6.9738 218.133 380.253 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 228.456 383.259 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 232.344 380.253 Tm
0.0006 Tc
(+1)Tj
ET
186.633 378.827 m
265.95 378.827 l
S
BT
6.9738 0 0 6.9738 186.633 372.8911 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F22 1 Tf
4.9813 0 0 4.9813 207.153 374.889 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 211.041 372.8911 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 238.662 374.889 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 242.541 372.8911 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0002 Tc
(+1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 362.52 403.752 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 367.569 399.738 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 372.042 401.232 Tm
-0.0004 Tc
(\(2\))Tj
/F1 1 Tf
2.3135 -0.4996 TD
0 Tc
()Tj
ET
395.091 396.26 m
454.869 396.26 l
S
BT
9.9626 0 0 9.9626 410.031 396.255 Tm
()Tj
0 0 TD
0.5005 Tc
()Tj
ET
424.975 396.255 m
424.975 426.144 l
S
BT
9.9626 0 0 9.9626 424.98 411.195 Tm
0 Tc
()Tj
0 1.5005 TD
()Tj
1.4996 -3.0001 TD
0.9996 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 361.413 380.415 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 367.101 379.416 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 370.989 380.415 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 376.677 379.416 Tm
(6)Tj
ET
361.413 378.827 m
380.565 378.827 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 361.413 372.612 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 367.101 375.015 Tm
(2)Tj
0 -0.9178 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 370.989 372.612 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 376.677 371.613 Tm
(3)Tj
/F2 1 Tf
9.9626 0 0 9.9626 384.525 376.329 Tm
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 398.187 381.162 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 425.808 384.168 Tm
(2)Tj
/F15 1 Tf
6.9738 0 0 6.9738 429.687 381.162 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0002 Tc
(+1\))Tj
ET
396.243 378.827 m
455.157 378.827 l
S
BT
6.9738 0 0 6.9738 396.243 372.8911 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F22 1 Tf
4.9813 0 0 4.9813 416.763 374.889 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 420.642 372.8911 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 427.851 374.889 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 431.739 372.8911 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0002 Tc
(+1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 143.343 331.023 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.252 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 148.392 327.018 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 152.865 328.512 Tm
-0.0004 Tc
(\(3\))Tj
/F1 1 Tf
2.3135 -0.5005 TD
2.4992 Tc
()Tj
ET
175.914 323.531 m
235.692 323.531 l
S
BT
9.9626 0 0 9.9626 190.8542 323.5261 Tm
0.9996 Tc
()Tj
ET
205.798 323.526 m
205.798 353.415 l
S
BT
9.9626 0 0 9.9626 205.794 338.475 Tm
0 Tc
()Tj
0 1.4996 TD
()Tj
1.5005 -3.0001 TD
0.9996 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 147.024 307.686 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 152.712 306.687 Tm
(3)Tj
ET
142.236 306.098 m
161.388 306.098 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 142.236 299.883 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 147.924 302.286 Tm
(2)Tj
0 -0.916 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 151.812 299.883 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 157.5 298.884 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 165.348 303.6 Tm
(=)Tj
/F14 1 Tf
6.9738 0 0 6.9738 185.328 307.524 Tm
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 189.423 310.53 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 193.311 307.524 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0006 Tc
(+1)Tj
ET
177.057 306.098 m
221.877 306.098 l
S
BT
6.9738 0 0 6.9738 177.057 300.162 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F22 1 Tf
4.9813 0 0 4.9813 197.577 302.16 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 201.465 300.162 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0002 Tc
(+1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 143.343 273.243 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 148.392 269.229 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 152.865 270.723 Tm
-0.0004 Tc
(\(1\))Tj
/F1 1 Tf
2.3135 -0.4996 TD
0 Tc
()Tj
0 0 TD
()Tj
ET
175.914 265.751 m
265.581 265.751 l
S
BT
9.9626 0 0 9.9626 190.8542 265.746 Tm
0.9996 Tc
()Tj
ET
220.747 265.746 m
220.747 280.695 l
S
BT
9.9626 0 0 9.9626 220.743 280.686 Tm
0 Tc
()Tj
0 -1.4996 TD
0.9998 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 154.908 249.906 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 160.596 248.907 Tm
0.0006 Tc
(18)Tj
ET
142.236 248.318 m
180.54 248.318 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 142.236 242.103 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 147.924 244.4971 Tm
(2)Tj
0 -0.916 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 151.812 242.103 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 157.5 241.104 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 161.388 242.103 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 167.076 241.104 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 170.964 242.103 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 176.652 241.104 Tm
(4)Tj
/F2 1 Tf
9.9626 0 0 9.9626 184.5 245.82 Tm
(=)Tj
/F14 1 Tf
6.9738 0 0 6.9738 231.876 249.744 Tm
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 235.971 252.75 Tm
(6)Tj
/F15 1 Tf
6.9738 0 0 6.9738 239.859 249.744 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 250.182 252.75 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 254.07 249.744 Tm
0.0006 Tc
(+1)Tj
ET
196.209 248.318 m
299.826 248.318 l
S
BT
6.9738 0 0 6.9738 196.209 242.382 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F22 1 Tf
4.9813 0 0 4.9813 216.729 244.371 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 220.617 242.382 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 248.238 244.371 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 252.117 242.382 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 282.744 244.371 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 286.623 242.382 Tm
0.0002 Tc
(+1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 362.52 273.243 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 367.569 269.229 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 372.042 270.723 Tm
-0.0004 Tc
(\(2\))Tj
/F1 1 Tf
2.3135 -0.4996 TD
0 Tc
()Tj
ET
395.091 265.751 m
484.758 265.751 l
S
BT
9.9626 0 0 9.9626 410.031 265.746 Tm
()Tj
0 0 TD
0.5005 Tc
()Tj
ET
439.924 265.746 m
439.924 280.695 l
S
BT
9.9626 0 0 9.9626 439.92 280.686 Tm
0 Tc
()Tj
0 -1.4996 TD
0.9998 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 364.509 249.906 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 370.197 248.907 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 374.085 249.906 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 379.773 248.907 Tm
0.0006 Tc
(10)Tj
ET
361.413 248.318 m
390.141 248.318 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 361.413 242.103 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 367.101 244.4971 Tm
(2)Tj
0 -0.916 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 370.989 242.103 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 376.677 241.104 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 380.565 242.103 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 386.253 241.104 Tm
(4)Tj
/F2 1 Tf
9.9626 0 0 9.9626 394.101 245.82 Tm
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 405.819 250.653 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 433.44 253.659 Tm
(4)Tj
/F15 1 Tf
6.9738 0 0 6.9738 437.319 250.653 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 447.642 253.659 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 451.521 250.653 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 461.736 253.659 Tm
(2)Tj
/F15 1 Tf
6.9738 0 0 6.9738 465.615 250.653 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0002 Tc
(+1\))Tj
ET
405.819 248.309 m
489.15 248.309 l
S
BT
6.9738 0 0 6.9738 405.882 242.382 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F22 1 Tf
4.9813 0 0 4.9813 426.402 244.371 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 430.281 242.382 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 437.49 244.371 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 441.378 242.382 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 472.005 244.371 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 475.875 242.382 Tm
0.0002 Tc
(+1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 143.343 215.4631 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 148.392 211.449 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 152.865 212.9431 Tm
-0.0004 Tc
(\(3\))Tj
/F1 1 Tf
2.3135 -0.5005 TD
2.4992 Tc
()Tj
ET
175.914 207.962 m
265.581 207.962 l
S
BT
9.9626 0 0 9.9626 190.8542 207.957 Tm
0.9996 Tc
()Tj
ET
220.747 207.957 m
220.747 222.906 l
S
BT
9.9626 0 0 9.9626 220.743 222.906 Tm
0 Tc
()Tj
0 -1.5005 TD
0.9998 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 137.061 192.117 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 142.749 191.1181 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 146.637 192.117 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 152.325 191.1181 Tm
(6)Tj
ET
132.273 190.529 m
161.001 190.529 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 132.273 184.314 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 137.961 186.717 Tm
(2)Tj
0 -0.916 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 141.849 184.314 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 147.537 183.3151 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 151.425 184.314 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 157.113 183.3151 Tm
(4)Tj
/F2 1 Tf
9.9626 0 0 9.9626 164.961 188.031 Tm
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 176.67 192.864 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 183.879 195.8701 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 187.767 192.864 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 218.394 195.8701 Tm
(2)Tj
/F15 1 Tf
6.9738 0 0 6.9738 222.273 192.864 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0002 Tc
(+1\))Tj
ET
176.67 190.529 m
245.79 190.529 l
S
BT
6.9738 0 0 6.9738 176.679 184.602 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F22 1 Tf
4.9813 0 0 4.9813 197.199 186.591 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 201.087 184.602 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 228.708 186.591 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 232.587 184.602 Tm
0.0002 Tc
(+1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 362.52 215.4631 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 367.569 211.449 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 372.042 212.9431 Tm
-0.0004 Tc
(\(4\))Tj
/F1 1 Tf
2.3135 -0.5005 TD
0 Tc
()Tj
ET
395.091 207.962 m
484.758 207.962 l
S
BT
9.9626 0 0 9.9626 410.031 207.957 Tm
2.5001 Tc
()Tj
1.5005 0 TD
0 Tc
()Tj
ET
439.924 207.957 m
439.924 222.906 l
S
BT
9.9626 0 0 9.9626 439.92 222.906 Tm
()Tj
0 -1.5005 TD
0.9998 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 361.413 192.117 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 367.101 191.1181 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 370.989 192.117 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 376.677 191.1181 Tm
(4)Tj
ET
361.413 190.529 m
380.565 190.529 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 361.413 184.314 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 367.101 186.717 Tm
(2)Tj
0 -0.916 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 370.989 184.314 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 376.677 183.3151 Tm
(3)Tj
/F2 1 Tf
9.9626 0 0 9.9626 384.525 188.031 Tm
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 403.344 192.864 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 430.965 195.8701 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 434.844 192.864 Tm
0.0002 Tc
(+1\))Tj
ET
396.243 190.529 m
455.157 190.529 l
S
BT
6.9738 0 0 6.9738 396.243 184.602 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F22 1 Tf
4.9813 0 0 4.9813 416.763 186.591 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 420.642 184.602 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 427.851 186.591 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 431.739 184.602 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0002 Tc
(+1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 143.343 157.674 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 148.392 153.6601 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 152.865 155.154 Tm
-0.0004 Tc
(\(5\))Tj
/F1 1 Tf
2.3135 -0.4996 TD
0 Tc
()Tj
4.4997 1.4996 TD
()Tj
ET
175.914 150.182 m
265.581 150.182 l
S
BT
9.9626 0 0 9.9626 190.854 150.177 Tm
0.9996 Tc
()Tj
ET
220.747 150.177 m
220.747 165.126 l
S
BT
9.9626 0 0 9.9626 220.743 165.117 Tm
0 Tc
()Tj
0 -1.4996 TD
0.9998 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 151.812 134.337 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 157.5 133.338 Tm
(8)Tj
ET
142.236 132.749 m
170.964 132.749 l
S
BT
/F13 1 Tf
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6.9738 0 0 6.9738 343.917 610.6801 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 349.605 609.681 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 353.493 610.6801 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 359.181 609.681 Tm
(3)Tj
/F2 1 Tf
9.9626 0 0 9.9626 367.029 614.397 Tm
(=)Tj
/F14 1 Tf
6.9738 0 0 6.9738 390.159 618.321 Tm
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 394.254 621.327 Tm
(4)Tj
/F13 1 Tf
6.9738 0 0 6.9738 398.142 618.321 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 408.357 621.327 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 412.236 618.321 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 422.451 621.327 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 426.339 618.321 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0006 Tc
(+1)Tj
ET
378.738 616.895 m
458.055 616.895 l
S
BT
6.9738 0 0 6.9738 378.738 610.968 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F22 1 Tf
4.9813 0 0 4.9813 399.258 612.957 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 403.146 610.968 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 430.767 612.957 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 434.646 610.968 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0002 Tc
(+1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 116.271 584.04 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 121.32 580.026 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 125.784 581.52 Tm
-0.0004 Tc
(\(5\))Tj
/F1 1 Tf
2.3135 -0.4996 TD
5.5002 Tc
()Tj
ET
148.833 576.548 m
253.449 576.548 l
S
BT
9.9626 0 0 9.9626 163.7822 576.543 Tm
0.9996 Tc
()Tj
ET
178.726 576.543 m
178.726 591.492 l
S
BT
9.9626 0 0 9.9626 178.722 591.483 Tm
0 Tc
()Tj
1.4996 -1.4996 TD
1.0001 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 105.201 560.703 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 110.889 559.704 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 114.777 560.703 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 120.465 559.704 Tm
(4)Tj
/F13 1 Tf
6.9738 0 0 6.9738 124.344 560.703 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 130.032 559.704 Tm
(8)Tj
ET
105.201 559.115 m
133.929 559.115 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 105.201 552.9 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 110.889 555.303 Tm
(2)Tj
0 -0.9178 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 114.777 552.9 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 120.465 551.901 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 124.344 552.9 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 130.032 551.901 Tm
(5)Tj
/F2 1 Tf
9.9626 0 0 9.9626 137.889 556.6171 Tm
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 175.905 561.4501 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 203.526 564.4561 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 207.405 561.4501 Tm
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 227.817 564.4561 Tm
(4)Tj
/F13 1 Tf
6.9738 0 0 6.9738 231.696 561.4501 Tm
0.0002 Tc
(+1\))Tj
ET
149.598 559.115 m
271.206 559.115 l
S
BT
6.9738 0 0 6.9738 149.598 553.179 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F22 1 Tf
4.9813 0 0 4.9813 170.118 555.177 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 174.006 553.179 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 181.215 555.177 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 185.094 553.179 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 215.721 555.177 Tm
(4)Tj
/F13 1 Tf
6.9738 0 0 6.9738 219.6 553.179 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 229.815 555.177 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 233.694 553.179 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 243.909 555.177 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 247.797 553.179 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0002 Tc
(+1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 335.448 584.04 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 340.497 580.026 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 344.97 581.52 Tm
-0.0004 Tc
(\(6\))Tj
/F1 1 Tf
2.3126 -0.4996 TD
0 Tc
()Tj
ET
368.01 576.548 m
472.626 576.548 l
S
BT
9.9626 0 0 9.9626 382.959 576.543 Tm
5.4993 Tc
()Tj
1.4996 0 TD
0 Tc
()Tj
ET
397.903 576.543 m
397.903 591.492 l
S
BT
9.9626 0 0 9.9626 397.899 591.483 Tm
()Tj
1.5005 -1.4996 TD
0.9998 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 337.428 560.703 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 343.116 559.704 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 347.004 560.703 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 352.692 559.704 Tm
0.0006 Tc
(12)Tj
ET
334.341 559.115 m
363.069 559.115 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 334.341 552.9 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 340.029 555.303 Tm
(2)Tj
0 -0.9178 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 343.917 552.9 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 349.605 551.901 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 353.493 552.9 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 359.181 551.901 Tm
(5)Tj
/F2 1 Tf
9.9626 0 0 9.9626 367.029 556.6171 Tm
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 395.991 561.4501 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 403.2 564.4561 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 407.088 561.4501 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 437.715 564.4561 Tm
(4)Tj
/F15 1 Tf
6.9738 0 0 6.9738 441.585 561.4501 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 451.908 564.4561 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 455.796 561.4501 Tm
0.0002 Tc
(+1\))Tj
ET
378.738 559.115 m
486.252 559.115 l
S
BT
6.9738 0 0 6.9738 378.738 553.179 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F22 1 Tf
4.9813 0 0 4.9813 399.258 555.177 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 403.146 553.179 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 430.767 555.177 Tm
(4)Tj
/F13 1 Tf
6.9738 0 0 6.9738 434.646 553.179 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 444.861 555.177 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 448.74 553.179 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 458.955 555.177 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 462.834 553.179 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0002 Tc
(+1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 116.271 526.26 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 121.32 522.246 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 125.784 523.7401 Tm
-0.0004 Tc
(\(7\))Tj
/F1 1 Tf
2.3135 -0.4996 TD
8.5003 Tc
()Tj
ET
148.833 518.759 m
253.449 518.759 l
S
BT
9.9626 0 0 9.9626 163.7822 518.7631 Tm
0.9996 Tc
()Tj
ET
178.726 518.763 m
178.726 533.712 l
S
BT
9.9626 0 0 9.9626 178.722 533.703 Tm
0 Tc
()Tj
1.4996 -1.4996 TD
1.0001 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 108.288 502.923 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 113.976 501.924 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 117.864 502.923 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 123.552 501.924 Tm
0.0006 Tc
(18)Tj
ET
105.201 501.335 m
133.929 501.335 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 105.201 495.111 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 110.889 497.514 Tm
(2)Tj
0 -0.916 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 114.777 495.111 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 120.465 494.112 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 124.344 495.111 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 130.032 494.112 Tm
(5)Tj
/F2 1 Tf
9.9626 0 0 9.9626 137.889 498.837 Tm
(=)Tj
/F13 1 Tf
6.9738 0 0 6.9738 180.945 503.67 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 208.566 506.676 Tm
(6)Tj
/F15 1 Tf
6.9738 0 0 6.9738 212.445 503.67 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 222.768 506.676 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 226.656 503.67 Tm
0.0002 Tc
(+1\))Tj
ET
149.598 501.326 m
271.206 501.326 l
S
BT
6.9738 0 0 6.9738 149.598 495.399 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F22 1 Tf
4.9813 0 0 4.9813 170.118 497.388 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 174.006 495.399 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 181.215 497.388 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 185.094 495.399 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 215.721 497.388 Tm
(4)Tj
/F13 1 Tf
6.9738 0 0 6.9738 219.6 495.399 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 229.815 497.388 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 233.694 495.399 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 243.909 497.388 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 247.797 495.399 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0002 Tc
(+1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 335.448 526.26 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 340.497 522.246 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 344.97 523.7401 Tm
-0.0004 Tc
(\(8\))Tj
/F1 1 Tf
2.3126 -0.4996 TD
0 Tc
()Tj
ET
368.01 518.759 m
472.626 518.759 l
S
BT
9.9626 0 0 9.9626 382.959 518.7631 Tm
8.4994 Tc
()Tj
1.4996 0 TD
0 Tc
()Tj
ET
397.903 518.763 m
397.903 533.712 l
S
BT
9.9626 0 0 9.9626 397.899 533.703 Tm
()Tj
1.5005 -1.4996 TD
0.9998 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 347.004 502.923 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 352.692 501.924 Tm
0.0006 Tc
(30)Tj
ET
334.341 501.335 m
372.645 501.335 l
S
BT
/F13 1 Tf
6.9738 0 0 6.9738 334.341 495.111 Tm
0 Tc
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 340.029 497.514 Tm
(2)Tj
0 -0.916 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 343.917 495.111 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 349.605 494.112 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 353.493 495.111 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 359.181 494.112 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 363.06 495.111 Tm
()Tj
/F22 1 Tf
4.9813 0 0 4.9813 368.748 494.112 Tm
(5)Tj
/F2 1 Tf
9.9626 0 0 9.9626 376.605 498.837 Tm
(=)Tj
/F14 1 Tf
6.9738 0 0 6.9738 416.826 502.761 Tm
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 420.921 505.767 Tm
(8)Tj
/F13 1 Tf
6.9738 0 0 6.9738 424.8 502.761 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 435.015 505.767 Tm
(7)Tj
/F15 1 Tf
6.9738 0 0 6.9738 438.903 502.761 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 449.226 505.767 Tm
(5)Tj
/F15 1 Tf
6.9738 0 0 6.9738 453.105 502.761 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 463.428 505.767 Tm
(4)Tj
/F15 1 Tf
6.9738 0 0 6.9738 467.316 502.761 Tm
()Tj
/F14 1 Tf
0.8931 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 477.639 505.767 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 481.518 502.761 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0006 Tc
(+1)Tj
ET
388.314 501.335 m
530.325 501.335 l
S
BT
6.9738 0 0 6.9738 388.314 495.399 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F22 1 Tf
4.9813 0 0 4.9813 408.834 497.388 Tm
0 Tc
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 412.722 495.399 Tm
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 440.343 497.388 Tm
(2)Tj
/F13 1 Tf
6.9738 0 0 6.9738 444.222 495.399 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 474.849 497.388 Tm
(4)Tj
/F13 1 Tf
6.9738 0 0 6.9738 478.719 495.399 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 488.934 497.388 Tm
(3)Tj
/F13 1 Tf
6.9738 0 0 6.9738 492.822 495.399 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
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-0.2331 -0.2529 TD
(D)Tj
/F14 1 Tf
6.9738 0 0 6.9738 199.098 683.391 Tm
(n)Tj
/F2 1 Tf
9.9626 0 0 9.9626 204.525 684.885 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
-0.0001 Tc
[(a,)-165.9(b)]TJ
/F2 1 Tf
1.4011 0 TD
0 Tc
(\))Tj
/F1 1 Tf
1.8383 1.5005 TD
()Tj
0 -3.0001 TD
()Tj
/F26 1 Tf
1 1.4996 TD
()Tj
-1 0.7498 TD
()Tj
1 -1.4996 TD
()Tj
-1 -0.7498 TD
()Tj
/F1 1 Tf
2.0001 1.4996 TD
()Tj
ET
0 0 0 1 K
0 J 0 j 0.405 w 10 M []0 d
1 i
260.595 684.89 m
270.558 684.89 l
S
BT
9.9626 0 0 9.9626 275.535 684.885 Tm
0.3001 Tc
()Tj
ET
290.484 684.89 m
300.447 684.89 l
S
BT
9.9626 0 0 9.9626 300.4471 684.885 Tm
0 Tc
()Tj
0 0 TD
()Tj
ET
300.447 684.89 m
310.41 684.89 l
S
BT
9.9626 0 0 9.9626 315.3873 684.885 Tm
0.3001 Tc
()Tj
ET
330.327 684.89 m
340.29 684.89 l
S
BT
9.9626 0 0 9.9626 340.2904 684.885 Tm
0 Tc
()Tj
2 1.5005 TD
()Tj
0 -3.0001 TD
()Tj
/F26 1 Tf
-2.0001 1.4996 TD
()Tj
1 0.7498 TD
()Tj
-1 -1.4996 TD
()Tj
1 -0.7498 TD
()Tj
/F6 1 Tf
1 1.4996 TD
(n)Tj
/F2 1 Tf
0.823 0 TD
0.2223 Tc
[(+1)-55.5(=)]TJ
/F6 1 Tf
2.833 0 TD
0 Tc
(a)Tj
/F2 1 Tf
0.7507 0 TD
(+)Tj
/F6 1 Tf
1 0 TD
(b)Tj
/F2 1 Tf
0.6513 0 TD
[(+)-222.3(1)-333.8(v)28.2(e)0(rtices,)-333.8(2)]TJ
/F18 1 Tf
6.5089 0 TD
()Tj
/F6 1 Tf
1.0551 0 TD
(a)Tj
/F18 1 Tf
0.8067 0 TD
()Tj
/F6 1 Tf
1.0552 0 TD
(b)Tj
ET
300.442 691.86 m
300.442 701.823 l
S
BT
/F26 1 Tf
9.9626 0 0 9.9626 300.447 691.86 Tm
()Tj
/F2 1 Tf
-6.0002 1.3 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(a)Tj
/F2 1 Tf
0.5285 0 TD
-0.0002 Tc
[(th)-334.5(from)-334(left,)]TJ
/F6 1 Tf
5.6696 0 TD
0 Tc
(b)Tj
/F2 1 Tf
0.4291 0 TD
-0.0003 Tc
[(th)-334.6(from)-334.1(righ)27.7(t\))]TJ
/F13 1 Tf
6.9738 0 0 6.9738 195.372 659.829 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F21 1 Tf
4.9813 0 0 4.9813 202.581 662.835 Tm
(a)Tj
/F24 1 Tf
0.7751 0 TD
()Tj
/F22 1 Tf
1.0841 0 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 215.721 659.829 Tm
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F21 1 Tf
4.9813 0 0 4.9813 236.133 662.835 Tm
(b)Tj
/F24 1 Tf
0.6342 0 TD
()Tj
/F22 1 Tf
1.0841 0 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 248.562 659.829 Tm
0.0002 Tc
(+1\))Tj
ET
195.372 657.494 m
261.774 657.494 l
S
BT
6.9738 0 0 6.9738 197.343 651.441 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0001 Tc
(1\)\()Tj
/F14 1 Tf
1.4622 0 TD
0 Tc
(z)Tj
/F21 1 Tf
4.9813 0 0 4.9813 225.072 653.4301 Tm
(a)Tj
/F22 1 Tf
0.7751 0 TD
(+)Tj
/F21 1 Tf
1.0281 0 TD
(b)Tj
/F24 1 Tf
0.6342 0 TD
()Tj
/F22 1 Tf
1.0841 0 TD
(2)Tj
/F15 1 Tf
6.9738 0 0 6.9738 246.483 651.441 Tm
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F6 1 Tf
9.9626 0 0 9.9626 262.962 654.996 Tm
0.1658 Tc
(, )Tj
/F2 1 Tf
1.2801 0 TD
0 Tc
(=)Tj
/F12 1 Tf
1.0552 0 TD
()Tj
/F2 1 Tf
-9.1729 -5.0472 TD
()Tj
/F6 1 Tf
-0.234 -0.2529 TD
(D)Tj
/F14 1 Tf
6.9738 0 0 6.9738 200.754 600.699 Tm
(n)Tj
/F2 1 Tf
9.9626 0 0 9.9626 206.19 602.1931 Tm
-0.0004 Tc
(\(0\))Tj
/F1 1 Tf
3.6271 1.5005 TD
0 Tc
()Tj
0 -3.0001 TD
()Tj
/F26 1 Tf
1 1.4996 TD
()Tj
-1 0.7507 TD
()Tj
1 -1.5005 TD
()Tj
-1 -0.7498 TD
()Tj
/F1 1 Tf
2.0001 1.4996 TD
()Tj
ET
262.251 602.198 m
272.214 602.198 l
S
BT
9.9626 0 0 9.9626 282.1771 602.1931 Tm
0.8 Tc
()Tj
ET
331.992 602.198 m
341.955 602.198 l
S
BT
9.9626 0 0 9.9626 341.9552 602.1931 Tm
0 Tc
()Tj
2.0001 1.5005 TD
()Tj
0 0 TD
()Tj
0 -3.0001 TD
()Tj
/F26 1 Tf
-2.0001 1.4996 TD
()Tj
1 0.7507 TD
()Tj
-1 -1.5005 TD
()Tj
1 -0.7498 TD
()Tj
/F6 1 Tf
1 1.4996 TD
(n)Tj
/F2 1 Tf
0.8221 0 TD
[(+)-222.3(1)-333.8(v)28.2(e)0(rtices,)]TJ
/F6 1 Tf
5.7311 0 TD
(n)Tj
/F18 1 Tf
0.8781 0 TD
()Tj
/F2 1 Tf
1.0551 0 TD
(4)Tj
/F14 1 Tf
6.9738 0 0 6.9738 220.662 576.228 Tm
(z)Tj
/F21 1 Tf
4.9813 0 0 4.9813 224.757 579.234 Tm
(n)Tj
/F24 1 Tf
0.8817 0 TD
()Tj
/F22 1 Tf
1.0841 0 TD
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 238.428 576.228 Tm
0.0006 Tc
(+1)Tj
ET
197.028 574.802 m
272.142 574.802 l
S
BT
6.9738 0 0 6.9738 197.028 568.875 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0001 Tc
(1\)\()Tj
/F14 1 Tf
1.4622 0 TD
0 Tc
(z)Tj
/F13 1 Tf
0.5872 0 TD
0.0001 Tc
(+1\)\()Tj
/F14 1 Tf
2.3398 0 TD
0 Tc
(z)Tj
/F21 1 Tf
4.9813 0 0 4.9813 245.169 570.864 Tm
(n)Tj
/F24 1 Tf
0.8817 0 TD
()Tj
/F22 1 Tf
1.0841 0 TD
(2)Tj
/F15 1 Tf
6.9738 0 0 6.9738 258.831 568.875 Tm
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F6 1 Tf
9.9626 0 0 9.9626 273.339 572.313 Tm
0.1658 Tc
(, )Tj
/F2 1 Tf
1.2801 0 TD
0 Tc
(=)Tj
/F12 1 Tf
1.0552 0 TD
()Tj
/F3 1 Tf
8.9664 0 0 8.9664 189.216 538.437 Tm
[(FIGURE)-277.9(7)]TJ
/F9 1 Tf
4.3341 0 TD
-0.0001 Tc
[(.)-456.4(T)-0.6(w)27.5(o)-341.4(of)-342.5(the)-342.9()-0.2(v)28.4(e)-341.9(innite)-343.9(families:)]TJ
15.7469 0.2529 TD
0 Tc
()Tj
/F7 1 Tf
-0.2379 -0.2529 TD
(D)Tj
/F20 1 Tf
5.9776 0 0 5.9776 374.733 537.438 Tm
(n)Tj
/F9 1 Tf
8.9664 0 0 8.9664 379.836 538.437 Tm
(\()Tj
/F7 1 Tf
0.3995 0 TD
-0.0005 Tc
[(a,)-172.7(b)]TJ
/F9 1 Tf
1.4424 0 TD
0.3421 Tc
[(\)a)342.1(n)342(d)]TJ
2.9782 0.2529 TD
0 Tc
()Tj
/F7 1 Tf
-0.2379 -0.2529 TD
(D)Tj
/F20 1 Tf
5.9776 0 0 5.9776 428.517 537.438 Tm
(n)Tj
/F9 1 Tf
8.9664 0 0 8.9664 433.62 538.437 Tm
-0.0002 Tc
(\(0\).)Tj
/F2 1 Tf
9.9626 0 0 9.9626 195.147 486.903 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2647 -0.252 TD
(A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 199.98 482.898 Tm
(2)Tj
/F14 1 Tf
0.5691 0 TD
(n)Tj
/F15 1 Tf
0.7059 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
(1)Tj
/F1 1 Tf
9.9626 0 0 9.9626 242.325 484.392 Tm
()Tj
T*
()Tj
ET
242.325 484.388 m
252.288 484.388 l
S
BT
9.9626 0 0 9.9626 262.2512 484.392 Tm
0.8 Tc
()Tj
ET
312.066 484.388 m
322.029 484.388 l
S
BT
9.9626 0 0 9.9626 322.0293 484.392 Tm
0 Tc
()Tj
ET
242.329 484.392 m
242.329 504.318 l
S
BT
9.9626 0 0 9.9626 242.325 504.3181 Tm
()Tj
ET
242.325 504.314 m
252.288 504.314 l
S
BT
9.9626 0 0 9.9626 262.251 504.3181 Tm
0.8 Tc
()Tj
ET
312.066 504.314 m
322.029 504.314 l
S
BT
9.9626 0 0 9.9626 322.0292 504.3181 Tm
0 Tc
()Tj
ET
322.033 484.392 m
322.033 504.318 l
S
BT
/F2 1 Tf
9.9626 0 0 9.9626 341.955 484.392 Tm
(2)Tj
/F6 1 Tf
0.4996 0 TD
(n)Tj
/F2 1 Tf
0.9341 0 TD
[(v)28.2(e)0(rtices,)]TJ
/F6 1 Tf
3.8972 0 TD
(n)Tj
/F18 1 Tf
0.8781 0 TD
()Tj
/F2 1 Tf
1.0551 0 TD
(2)Tj
/F14 1 Tf
6.9738 0 0 6.9738 210.456 458.427 Tm
(z)Tj
/F21 1 Tf
4.9813 0 0 4.9813 214.551 461.433 Tm
(n)Tj
/F13 1 Tf
6.9738 0 0 6.9738 219.438 458.427 Tm
0.0006 Tc
(+1)Tj
ET
197.028 457.001 m
242.955 457.001 l
S
BT
6.9738 0 0 6.9738 197.028 451.065 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0001 Tc
(1\)\()Tj
/F14 1 Tf
1.4622 0 TD
0 Tc
(z)Tj
/F21 1 Tf
4.9813 0 0 4.9813 224.757 453.054 Tm
(n)Tj
/F15 1 Tf
6.9738 0 0 6.9738 229.635 451.065 Tm
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F6 1 Tf
9.9626 0 0 9.9626 244.143 454.503 Tm
0.1658 Tc
(, )Tj
/F2 1 Tf
1.2801 0 TD
0 Tc
(=)Tj
/F12 1 Tf
1.0552 0 TD
()Tj
/F3 1 Tf
8.9664 0 0 8.9664 256.311 420.627 Tm
[(FIGURE)-277.9(8)]TJ
/F9 1 Tf
4.3341 0 TD
0.3434 Tc
[(.)-112.9(R)343.1(o)315.3(o)343.4(t)343.6(e)343.9(de)343.9(v)371.9(e)343.9(nc)343.5(y)343.8(c)343.5(l)343.8(e)343.9(s)343.3(.)]TJ
/F3 1 Tf
9.9626 0 0 9.9626 63 388.992 Tm
-0.0003 Tc
[(7.)-1201.1(A)-278.2(C)0(OMPLETE)-279.9(DESCRIPTION)-280.2(OF)-279(SALEM)-279.4(TREES)]TJ
/F2 1 Tf
0 -1.8998 TD
-0.0001 Tc
[(In)-417.5(this)-417.8(section)-418.4(w)28.3(e)-417.5(consider)-417.9(the)-418.4(c)-0.1(ase)-417.5(o)0.3(f)-417.2(t)0.3(hose)-418.4(\(of)-418.2(course)]TJ
0 -1.3 TD
[(bipartite\))-428.8(S)-0.1(alem)-427.9(g)0.3(raphs)-427.7(dened)-427.4(b)27.9(y)-427.2(trees.)-726(A)0.1(s)-426.8(b)-28.1(efore,)-450.4(if)]TJ
/F6 1 Tf
T*
0 Tc
(T)Tj
/F2 1 Tf
1.0804 0 TD
-0.0001 Tc
[(is)-357.3(a)-357.4(r)-0.5(o)-27.7(oted)-357.9(t)0.3(ree,)-362.8(then)]TJ
/F6 1 Tf
9.6635 0 TD
0 Tc
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 177.246 347.781 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 183.6 344.163 Tm
-0.0002 Tc
[(will)-358.4(denote)-358(the)-358(r)-0.6(o)-27.8(oted)-358(f)0(orest)]TJ
-12.1052 -1.3 TD
-0.0001 Tc
[(obtained)-443.7(b)27.9(y)-442.6(deleting)-444.1(t)0.3(he)-442.8(ro)-27.7(ot)]TJ
/F6 1 Tf
13.6863 0 TD
0 Tc
(r)Tj
/F2 1 Tf
0.9214 0 TD
-0.0004 Tc
(of)Tj
/F6 1 Tf
1.2476 0 TD
0 Tc
(T)Tj
/F2 1 Tf
0.7236 0 TD
-0.0003 Tc
[(,)-469.6(with)-443.9(the)-443(r)-0.7(o)-27.9(o)0.1(t)-442.5(o)0.1(f)]TJ
-16.5789 -1.3 TD
-0.0001 Tc
[(eac)27.9(h)-366.9(subtree)-366.9(b)-28.1(eing)-366.4(the)-366.9(v)28.1(ertex)-367.6(t)0.3(hat)-367.3(\(in)]TJ
/F6 1 Tf
17.1607 0 TD
0 Tc
(T)Tj
/F2 1 Tf
0.7236 0 TD
-0.0001 Tc
[(\))-366.4(i)0.3(s)-367.2(a)0.3(djacen)27.9(t)-367.3(t)0.3(o)]TJ
/F6 1 Tf
-17.8843 -1.3 TD
0 Tc
(r)Tj
/F2 1 Tf
0.4788 0 TD
-0.0001 Tc
[(.)-699.8(T)0.3(he)-418.4(quotien)27.9(t)-420.6(of)-418.2(a)-418.8(r)-0.5(o)-27.7(oted)-419.3(f)0.1(orest)-417.9(i)0.3(s)-418.7(dened)-418.4(to)-418.8(b)-28.1(e)-418.4(the)]TJ
-0.4788 -1.3 TD
[(sum)-314.1(o)0.3(f)-315.2(t)0.3(he)-314.5(quotien)27.9(t)0.3(s)-316.6(o)0.3(f)-314.3(its)-315.7(ro)-27.7(oted)-315.4(t)0.3(rees.)-437.8(F)82.6(or)-314(ro)-27.7(oted)-315.4(t)0.3(rees)]TJ
/F6 1 Tf
T*
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 68.823 277.914 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 75.87 279.408 Tm
-0.0002 Tc
(and)Tj
/F6 1 Tf
1.87 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 100.323 277.914 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 104.787 279.408 Tm
-0.0001 Tc
[(,)-274.3(w)28.3(e)-259.4(dene)-258.5(the)-259.4(r)-0.5(o)-27.7(oted)-259.4(t)0.3(ree)]TJ
/F6 1 Tf
11.4061 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 224.244 277.914 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 229.437 279.408 Tm
(+)Tj
/F6 1 Tf
0.851 0 TD
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 243.738 277.914 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 250.785 279.408 Tm
-0.0001 Tc
[(to)-258.9(b)-28.1(e)-258.5(the)-259.4(t)0.3(ree)]TJ
-18.8489 -1.3 TD
-0.0002 Tc
[(obtained)-400.4(b)27.8(y)-399.3(joining)-400.9(t)0.2(he)-399.5(ro)-27.8(ots)-399.8(of)]TJ
/F6 1 Tf
14.596 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 214.236 264.963 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 222.678 266.457 Tm
-0.0002 Tc
(and)Tj
/F6 1 Tf
2.01 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 248.526 264.963 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 256.959 266.457 Tm
-0.0002 Tc
[(b)27.8(y)-399.3(an)-399.5(edge,)]TJ
-19.4686 -1.3 TD
[(and)-333.6(making)-335.8(t)0.2(he)-333.6(ro)-27.8(ot)-334(of)]TJ
/F6 1 Tf
10.4748 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 173.178 252.0121 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 180.972 253.506 Tm
-0.0002 Tc
[(its)-333.9(ro)-27.8(ot.)]TJ
/F3 1 Tf
-11.8414 -2.5999 TD
[(Lemma)-278.9(7.1.)]TJ
/F11 1 Tf
0.3758 -1.7661 TD
-0.0001 Tc
(\(i\))Tj
/F2 1 Tf
1.6243 0 TD
-0.0002 Tc
[([McKee)-399.5(et)-400(al.)-644.8(99,)-417.1(Corollary)-402(4)0.2(])]TJ
/F11 1 Tf
14.016 0 TD
-0.0514 Tc
[(F)25(o)-51.6(r)-469.9(a)-469.9(roo)-51.6(t)-51.6(e)0.3(d)-470.8(t)-51.6(ree)]TJ
/F6 1 Tf
7.8613 0 TD
0 Tc
(T)Tj
/F11 1 Tf
-21.8773 -1.3 TD
0.0001 Tc
[(with)-486.1(r)51.4(o)51.4(ote)51.8(d)-487(s)-0.2(ubtr)51.4(e)51.8(e)0.3(s)]TJ
/F6 1 Tf
9.2534 0 TD
0 Tc
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 182.322 200.676 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 190.206 197.0581 Tm
(=)Tj
/F12 1 Tf
1.2891 0 TD
({)Tj
/F6 1 Tf
0.4996 0 TD
(T)Tj
/F14 1 Tf
6.9738 0 0 6.9738 213.849 195.564 Tm
(i)Tj
/F12 1 Tf
9.9626 0 0 9.9626 217.17 197.0581 Tm
(})Tj
/F11 1 Tf
0.4996 0 TD
[(,)-519(i)0.4(ts)-486.4(quotient)]TJ
/F6 1 Tf
6.3472 0 TD
(q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 289.827 194.1331 Tm
(T)Tj
/F11 1 Tf
9.9626 0 0 9.9626 300.951 197.0581 Tm
-0.0004 Tc
(is)Tj
-21.8843 -1.3 TD
-0.0001 Tc
[(given)-358.4(r)51.2(e)51.6(cursively)-359.2(b)0.1(y)]TJ
/F6 1 Tf
2.9098 -2.197 TD
0 Tc
(q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 116.361 159.294 Tm
(T)Tj
/F2 1 Tf
9.9626 0 0 9.9626 125.406 162.219 Tm
(=)Tj
3.5801 0.6766 TD
(1)Tj
ET
137.115 164.717 m
190.017 164.717 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 137.115 155.388 Tm
(z)Tj
/F2 1 Tf
0.7317 0 TD
0.2223 Tc
(+1)Tj
/F12 1 Tf
1.7218 0 TD
0 Tc
()Tj
/F6 1 Tf
1 0 TD
0.0445 Tc
(zq)Tj
/F14 1 Tf
6.9738 0 0 6.9738 181.044 152.454 Tm
0 Tc
(T)Tj
/F24 1 Tf
4.9813 0 0 4.9813 186.822 154.452 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 193.977 162.219 Tm
(=)Tj
4.4103 0.6766 TD
(1)Tj
ET
205.686 164.717 m
275.13 164.717 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 205.686 155.388 Tm
(z)Tj
/F2 1 Tf
0.7317 0 TD
0.2223 Tc
(+1)Tj
/F12 1 Tf
1.7219 0 TD
0 Tc
()Tj
/F6 1 Tf
1 0 TD
(z)Tj
/F23 1 Tf
0.6757 0.7498 TD
()Tj
/F14 1 Tf
6.9738 0 0 6.9738 257.346 152.4001 Tm
(i)Tj
/F6 1 Tf
9.9626 0 0 9.9626 262.323 155.388 Tm
(q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 266.769 152.454 Tm
(T)Tj
/F21 1 Tf
4.9813 0 0 4.9813 271.476 151.4551 Tm
(i)Tj
/F6 1 Tf
9.9626 0 0 9.9626 276.318 162.219 Tm
(,)Tj
/F11 1 Tf
-19.4117 -2.5114 TD
0.0001 Tc
(with)Tj
/F6 1 Tf
2.1717 0 TD
0 Tc
(q)Tj
/F15 1 Tf
6.9738 0 0 6.9738 109.008 135.7051 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 116.361 137.199 Tm
0.2774 Tc
(=1)Tj
/F6 1 Tf
1.5547 0 TD
0 Tc
(/)Tj
/F2 1 Tf
0.4996 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.7326 0 TD
0.2223 Tc
[(+1)222.7(\))]TJ
/F11 1 Tf
2.2467 0 TD
0 Tc
[(for)-358(the)-357.6(single-vertex)-359.1(t)-0.2(r)51.3(e)51.7(e)]TJ
/F12 1 Tf
10.9545 0 TD
()Tj
/F11 1 Tf
0.4996 0 TD
(.)Tj
-22.1636 -1.9332 TD
[(\(ii\))-500.8(F)76.4(o)-0.2(r)-357.1(the)-357.6(r)51.3(o)51.3(ote)51.7(d)-357.9(t)-0.2(r)51.3(e)51.7(e)]TJ
/F6 1 Tf
10.3401 0 TD
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 172.521 116.4451 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 179.208 117.939 Tm
(+)Tj
/F6 1 Tf
1 0 TD
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 194.994 116.4451 Tm
(2)Tj
/F11 1 Tf
9.9626 0 0 9.9626 203.022 117.939 Tm
0.0002 Tc
[(we)-357.4(have)]TJ
/F6 1 Tf
-14.4549 -2.655 TD
0 Tc
(q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 63.459 88.563 Tm
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 68.166 87.564 Tm
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 72.054 88.563 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 82.881 87.564 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 90.036 91.488 Tm
(=)Tj
/F6 1 Tf
2.9703 0.7841 TD
(q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 124.074 96.366 Tm
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 128.781 95.367 Tm
(1)Tj
ET
101.745 93.977 m
151.056 93.977 l
S
BT
/F2 1 Tf
9.9626 0 0 9.9626 101.745 84.657 Tm
(1)Tj
/F12 1 Tf
0.7218 0 TD
()Tj
/F6 1 Tf
1 0 TD
0.0445 Tc
(zq)Tj
/F14 1 Tf
6.9738 0 0 6.9738 128.421 81.7231 Tm
0 Tc
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 133.128 80.724 Tm
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 137.511 84.657 Tm
(q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 141.957 81.7231 Tm
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 146.664 80.724 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 155.016 91.488 Tm
(=)Tj
/F6 1 Tf
5.4799 0.9413 TD
(z)Tj
/F2 1 Tf
0.7308 0 TD
0.2223 Tc
(+1)Tj
/F12 1 Tf
1.7218 0 TD
0 Tc
()Tj
/F6 1 Tf
1 0 TD
0.0445 Tc
(zq)Tj
/F14 1 Tf
6.9738 0 0 6.9738 253.53 97.536 Tm
0 Tc
(T)Tj
/F24 1 Tf
4.9813 0 0 4.9813 259.308 99.939 Tm
()Tj
/F22 1 Tf
-0.215 -0.916 TD
(2)Tj
ET
166.725 93.977 m
305.505 93.977 l
S
BT
/F2 1 Tf
9.9626 0 0 9.9626 166.725 84.657 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.7317 0 TD
0.2223 Tc
(+1)Tj
/F12 1 Tf
1.7218 0 TD
0 Tc
()Tj
/F6 1 Tf
1 0 TD
0.0445 Tc
(zq)Tj
/F14 1 Tf
6.9738 0 0 6.9738 214.524 81.3181 Tm
0 Tc
(T)Tj
/F24 1 Tf
4.9813 0 0 4.9813 220.302 83.721 Tm
()Tj
/F22 1 Tf
-0.215 -0.916 TD
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 223.614 84.657 Tm
-0.0004 Tc
(\)\()Tj
/F6 1 Tf
0.7769 0 TD
0 Tc
(z)Tj
/F2 1 Tf
0.7326 0 TD
0.2223 Tc
(+1)Tj
/F12 1 Tf
1.7218 0 TD
0 Tc
()Tj
/F6 1 Tf
1 0 TD
0.0445 Tc
(zq)Tj
/F14 1 Tf
6.9738 0 0 6.9738 275.292 81.3181 Tm
0 Tc
(T)Tj
/F24 1 Tf
4.9813 0 0 4.9813 281.07 83.721 Tm
()Tj
/F22 1 Tf
-0.215 -0.916 TD
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 284.382 84.657 Tm
(\))Tj
/F12 1 Tf
0.6107 0 TD
()Tj
/F6 1 Tf
1 0 TD
(z)Tj
0.6296 0.6857 TD
(.)Tj
/F11 1 Tf
1.9386 29.862 TD
-0.0513 Tc
[(P)-51.4(roo)-51.5(f)-348.1(o)-51.5(f)-347.2(\()-51.7(i)-50.9(i)-50.9(\))-51.7(:)]TJ
/F2 1 Tf
5.9045 0 TD
-0.0002 Tc
[(Applying)-268.1(\(i\))-268.1(to)]TJ
/F6 1 Tf
6.7447 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 457.857 387.498 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 463.221 388.992 Tm
(+)Tj
/F6 1 Tf
0.8672 0 TD
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 477.684 387.498 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 484.803 388.992 Tm
-0.0002 Tc
[(and)-267.6(t)0.2(hen)-267.6(to)]TJ
/F6 1 Tf
5.2451 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 542.88 387.498 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 550.0079 388.992 Tm
-0.0002 Tc
[(giv)28(es)]TJ
/F6 1 Tf
-20.1046 -2.7011 TD
0 Tc
(q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 354.159 359.157 Tm
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 358.866 358.158 Tm
(1)Tj
/F13 1 Tf
6.9738 0 0 6.9738 362.754 359.157 Tm
(+)Tj
/F14 1 Tf
0.8776 0 TD
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 373.581 358.158 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 380.727 362.082 Tm
(=)Tj
5.1312 0.6766 TD
(1)Tj
ET
392.436 364.58 m
476.244 364.58 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 392.436 355.251 Tm
(z)Tj
/F2 1 Tf
0.7317 0 TD
0.2223 Tc
(+1)Tj
/F12 1 Tf
1.7218 0 TD
0 Tc
()Tj
/F6 1 Tf
1 0 TD
0.0445 Tc
(zq)Tj
/F14 1 Tf
6.9738 0 0 6.9738 436.365 351.9211 Tm
0 Tc
(T)Tj
/F24 1 Tf
4.9813 0 0 4.9813 442.143 354.324 Tm
()Tj
/F22 1 Tf
-0.215 -0.916 TD
(1)Tj
/F12 1 Tf
9.9626 0 0 9.9626 447.669 355.251 Tm
()Tj
/F6 1 Tf
1 0 TD
0.0445 Tc
(zq)Tj
/F14 1 Tf
6.9738 0 0 6.9738 467.154 352.326 Tm
0 Tc
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 471.861 351.327 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 480.204 362.082 Tm
(=)Tj
3.6505 0.6766 TD
(1)Tj
ET
491.913 364.58 m
546.21 364.58 l
S
BT
9.9626 0 0 9.9626 491.913 355.251 Tm
(1)Tj
/F6 1 Tf
0.4996 0 TD
-0.0004 Tc
(/q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 506.313 352.326 Tm
0 Tc
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 511.02 351.327 Tm
(1)Tj
/F12 1 Tf
9.9626 0 0 9.9626 517.635 355.251 Tm
()Tj
/F6 1 Tf
0.9991 0 TD
0.0445 Tc
(zq)Tj
/F14 1 Tf
6.9738 0 0 6.9738 537.111 352.326 Tm
0 Tc
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 541.818 351.327 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 380.727 330.177 Tm
(=)Tj
/F6 1 Tf
2.9703 0.7832 TD
(q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 414.765 335.0551 Tm
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 419.472 334.056 Tm
(1)Tj
ET
392.436 332.666 m
441.747 332.666 l
S
BT
/F2 1 Tf
9.9626 0 0 9.9626 392.436 323.337 Tm
(1)Tj
/F12 1 Tf
0.7227 0 TD
()Tj
/F6 1 Tf
1 0 TD
0.0445 Tc
(zq)Tj
/F14 1 Tf
6.9738 0 0 6.9738 419.121 320.412 Tm
0 Tc
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 423.828 319.413 Tm
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 428.202 323.337 Tm
(q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 432.648 320.412 Tm
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 437.355 319.413 Tm
(2)Tj
/F6 1 Tf
9.9626 0 0 9.9626 444.6 330.177 Tm
(.)Tj
/F2 1 Tf
-11.9029 -2.9604 TD
-0.0003 Tc
[(No)28.1(w)-392.9(a)0.1(pplying)-392.8(\(i\))-392.8(again)-393.3(to)-391.9(b)-28.3(oth)]TJ
/F6 1 Tf
14.3485 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 474.786 299.19 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 483.156 300.684 Tm
-0.0002 Tc
(and)Tj
/F6 1 Tf
2.0028 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 508.932 299.19 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 517.302 300.684 Tm
-0.0003 Tc
[(giv)27.9(es)-392.7(the)-392.4(a)0.1(l-)]TJ
-19.2003 -1.3 TD
-0.0002 Tc
[(ternativ)28(e)-335.4(f)0(orm)28.2(u)-0.2(la.)]TJ
ET
564.318 290.924 m
571.095 290.924 l
564.521 284.745 m
564.521 290.73 l
570.901 284.745 m
570.901 290.73 l
564.318 284.552 m
571.095 284.552 l
S
BT
9.9626 0 0 9.9626 337.968 264.369 Tm
-0.0003 Tc
[(Note)-341.8(that)-342.2(\(i\))-341.3(implies)-343(t)0.1(hat)]TJ
/F6 1 Tf
11.5706 0 TD
0 Tc
( )Tj
/F2 1 Tf
0.5574 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(T)Tj
/F2 1 Tf
0.7236 0 TD
0.2898 Tc
(\)=1)Tj
/F6 1 Tf
2.2458 0 TD
0 Tc
(/)Tj
/F2 1 Tf
0.4996 0 TD
-0.0004 Tc
(\(2)Tj
/F12 1 Tf
1.1175 0 TD
0 Tc
()Tj
/F6 1 Tf
1.0046 0 TD
( )Tj
/F2 1 Tf
0.5574 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 534.996 267.9871 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 537.795 264.369 Tm
-0.0004 Tc
[(\)\),)-344.1(with)]TJ
/F6 1 Tf
-21.2573 -1.3 TD
0 Tc
( )Tj
/F2 1 Tf
0.5574 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 342.648 255.036 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 345.447 251.418 Tm
0.2778 Tc
(\)=)Tj
/F23 1 Tf
1.7218 0.7498 TD
0 Tc
()Tj
/F14 1 Tf
6.9738 0 0 6.9738 373.122 248.43 Tm
(i)Tj
/F6 1 Tf
9.9626 0 0 9.9626 378.099 251.418 Tm
( )Tj
/F2 1 Tf
0.5574 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(T)Tj
/F14 1 Tf
6.9738 0 0 6.9738 393.345 249.924 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 396.666 251.418 Tm
-0.0004 Tc
(\).)Tj
-5.8918 -1.3 TD
-0.0001 Tc
[(The)-431(next)-430.6(t)0.3(heorem)-430.6(describ)-28.1(es)-429.5(all)-431.5(Salem)-431.5(t)0.3(rees.)-735(F)82.6(or)-429.6(an)]TJ
-1.1997 -1.3 TD
-0.0002 Tc
[(alternativ)28(e)-302.9(a)0.2(pproac)27.8(h)-301(t)0.2(o)-301.5(a)-300.6(generalisation)-302.9(of)-300.8(this)-301.4(topic,)-307.8(s)-0.5(ee)]TJ
T*
[(Neumaier)-334.9([)0.2(Neumaier)-335.8(82,)-334(Theorem)-334(2.6].)]TJ
/F3 1 Tf
0 -2.5999 TD
-0.0003 Tc
[(T)37.2(heor)11.1(em)-279.4(7.2.)]TJ
/F11 1 Tf
0.3749 -2.1302 TD
0.0002 Tc
[(\(i\))-500.6(S)0.5(upp)51.5(o)0(se)-403.4(that)]TJ
/F6 1 Tf
7.5695 0 TD
0 Tc
(T)Tj
/F11 1 Tf
1.1274 0 TD
-0.0514 Tc
[(i)-51(s)-455.6(a)-455.4(roo)-51.6(t)-51.6(e)0.3(d)-456.3(t)-51.6(ree)-455.9(w)-51.9(i)-51(t)-51.6(h)]TJ
/F6 1 Tf
9.2263 0 TD
0 Tc
( )Tj
/F2 1 Tf
0.5574 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 524.943 169.0501 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 527.742 165.441 Tm
(\))Tj
/F6 1 Tf
0.7507 0 TD
(>)Tj
/F2 1 Tf
1.1392 0 TD
(2)Tj
/F11 1 Tf
0.4996 0 TD
0.416 Tc
[(,f)416.4(o)415.8(r)]TJ
-20.6376 -1.3 TD
0.0001 Tc
[(which)-272(the)-272.5(for)51.4(e)0.3(st)]TJ
/F6 1 Tf
6.9642 0 TD
0 Tc
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 422.532 156.099 Tm
()Tj
/F11 1 Tf
9.9626 0 0 9.9626 428.04 152.4901 Tm
[(is)-273.2(a)-273(c)51.7(ol)-51.6(le)51.7(ction)-273.4(o)-0.2(f)-272.4(c)0.2(yclotomic)-273.5(tr)51.3(e)51.7(e)0.2(s.)]TJ
-8.2406 -1.3009 TD
-0.0001 Tc
(Then)Tj
/F6 1 Tf
2.5051 0 TD
0 Tc
(T)Tj
/F11 1 Tf
0.9793 0 TD
[(is)-256(a)-256.8(S)0.3(alem)-255.5(tr)51.3(e)51.7(e)0.2(.)-426.9(\()-0.3(If)]TJ
/F6 1 Tf
8.2633 0 TD
( )Tj
/F2 1 Tf
0.5574 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 479.61 143.1481 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 482.409 139.5301 Tm
(\))Tj
/F18 1 Tf
0.6667 0 TD
()Tj
/F2 1 Tf
1.0552 0 TD
(2)Tj
/F11 1 Tf
0.7561 0 TD
0.0001 Tc
(then)Tj
/F6 1 Tf
2.1221 0 TD
0 Tc
(T)Tj
/F11 1 Tf
0.9793 0 TD
-0.0002 Tc
[(is)-256.2(again)]TJ
-19.2772 -1.3 TD
-0.0001 Tc
[(a)-357.1(c)0.1(yclotomic)-359.5(tr)51.2(e)51.6(e)0.1(.\))]TJ
-1.9314 -2.16 TD
0 Tc
[(\(ii\))-500.8(Supp)51.3(ose)-419.9(that)]TJ
/F6 1 Tf
7.9082 0 TD
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 411.309 103.566 Tm
(1)Tj
/F11 1 Tf
9.9626 0 0 9.9626 419.967 105.0601 Tm
-0.0001 Tc
(and)Tj
/F6 1 Tf
2.0055 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 445.77 103.566 Tm
(2)Tj
/F11 1 Tf
9.9626 0 0 9.9626 454.419 105.0601 Tm
-0.0001 Tc
[(ar)51.2(e)-420.9(S)0.2(alem)-420.9(tr)51.2(e)51.6(e)0.1(s)-421.4(o)-0.3(f)-419.7(t)-0.3(yp)51.2(e)-420.9(\()-0.5(i\))]TJ
-10.8884 -1.3 TD
0.0001 Tc
(with)Tj
/F2 1 Tf
2.1889 0 TD
0 Tc
(\()Tj
/F6 1 Tf
0.3885 0 TD
( )Tj
/F2 1 Tf
0.5574 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 388.251 95.727 Tm
()Tj
/F13 1 Tf
-0.1987 -0.8737 TD
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 391.347 92.109 Tm
(\))Tj
/F12 1 Tf
0.6233 0 TD
()Tj
/F2 1 Tf
1.0118 0 TD
-0.0004 Tc
(2\)\()Tj
/F6 1 Tf
1.2765 0 TD
0 Tc
( )Tj
/F2 1 Tf
0.5574 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 436.986 95.727 Tm
()Tj
/F13 1 Tf
-0.1987 -0.8737 TD
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 440.091 92.109 Tm
(\))Tj
/F12 1 Tf
0.6233 0 TD
()Tj
/F2 1 Tf
1.0127 0 TD
-0.0004 Tc
(2\))Tj
/F18 1 Tf
1.197 0 TD
0 Tc
()Tj
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[(has)-379.1(n)-0.2(one.)-577.9(This)-378.1(giv)28(es)]TJ
-13.4169 -1.3009 TD
-0.0001 Tc
[(the)-333.5()-0.1(rst)-333(r)-0.5(esult.)]TJ
-1.833 -2.235 TD
-0.0003 Tc
[(\(ii\))-501.2(Let)]TJ
/F6 1 Tf
3.6533 0 TD
0 Tc
(T)Tj
/F2 1 Tf
1.0488 0 TD
(=)Tj
/F6 1 Tf
1.1039 0 TD
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 106.236 198.8851 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 113.103 200.379 Tm
(+)Tj
/F6 1 Tf
1.0199 0 TD
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 129.087 198.8851 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 133.551 200.379 Tm
0.5307 Tc
[(.T)614.2(a)531.1(k)558.9(e)]TJ
/F6 1 Tf
3.254 0 TD
0.3259 Tc
(>)Tj
/F2 1 Tf
1.8953 0 TD
-0.0001 Tc
[(0)-361.9(s)-0.4(uc)27.9(h)-362.4(t)0.3(hat)-362.8(neither)]TJ
/F6 1 Tf
8.7619 0 TD
0 Tc
(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 279.711 198.8851 Tm
(T)Tj
/F2 1 Tf
9.9626 0 0 9.9626 60.831 187.4281 Tm
-0.0002 Tc
(nor)Tj
/F6 1 Tf
1.7074 0 TD
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(R)Tj
/F14 1 Tf
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(T)Tj
/F24 1 Tf
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()Tj
/F2 1 Tf
9.9626 0 0 9.9626 96.966 187.4281 Tm
-0.0553 Tc
[(va)-54.9(n)-55.3(i)-54.9(s)-55.6(h)-315.5(o)-54.9(n)]TJ
/F6 1 Tf
4.3317 0 TD
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(I)Tj
/F2 1 Tf
0.7959 0 TD
0.2774 Tc
[(=\()277.8(1)]TJ
/F6 1 Tf
1.9432 0 TD
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(,)Tj
/F2 1 Tf
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0.0755 Tc
(1+)Tj
/F6 1 Tf
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()Tj
/F2 1 Tf
0.4661 0 TD
-0.0003 Tc
[(\).)-422.6(No)28.1(w)]TJ
/F6 1 Tf
3.2928 0 TD
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(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 230.724 191.046 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 236.115 187.4281 Tm
-0.0001 Tc
[(is)-260.6(the)-260.3(f)0.1(orest)]TJ
/F12 1 Tf
-17.5941 -1.3 TD
0 Tc
({)Tj
/F6 1 Tf
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(T)Tj
/F15 1 Tf
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()Tj
/F13 1 Tf
-0.1987 -0.8737 TD
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 76.104 174.477 Tm
0.1658 Tc
(,T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 86.346 172.983 Tm
0 Tc
(2)Tj
/F12 1 Tf
9.9626 0 0 9.9626 90.819 174.477 Tm
(})Tj
/F2 1 Tf
0.4996 0 TD
-0.0002 Tc
[(,)-331.3(s)-0.5(o)-330.4(t)0.2(hat)]TJ
/F6 1 Tf
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(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 143.19 172.983 Tm
(T)Tj
/F24 1 Tf
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()Tj
/F2 1 Tf
9.9626 0 0 9.9626 155.439 174.477 Tm
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[(has)-331.2(o)0.2(ne)-330.9(ro)-27.8(ot)-330.4(on)-330.9(\(1)]TJ
/F6 1 Tf
8.023 0 TD
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(,)Tj
/F12 1 Tf
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()Tj
/F2 1 Tf
1 0 TD
-0.0004 Tc
[(\),)-333.3(a)-329.7(r)-0.8(o)-28(o)0(t)]TJ
-18.9628 -1.3 TD
(of)Tj
/F6 1 Tf
1.1599 0 TD
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(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 79.956 160.032 Tm
(T)Tj
/F22 1 Tf
4.9813 0 0 4.9813 84.663 159.0331 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 89.037 161.526 Tm
-0.0002 Tc
[(.)-507.5(B)-0.1(y)-355(i)0.2(n)27.8(t)0.2(erlacing,)]TJ
/F6 1 Tf
7.5993 0 TD
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(R)Tj
/F14 1 Tf
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(T)Tj
/F2 1 Tf
9.9626 0 0 9.9626 182.115 161.526 Tm
-0.0002 Tc
[(has)-354.7(o)0.2(ne)-354.3(or)-354.7(t)28.2(w)28.2(o)-355.7(ro)-27.8(ots)-355.6(on)]TJ
-12.1739 -1.3 TD
[(that)-334(in)27.8(terv)55.1(al.)]TJ
0 -1.7679 TD
0 Tc
(On)Tj
/F6 1 Tf
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(I)Tj
/F2 1 Tf
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(,)Tj
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(R)Tj
/F14 1 Tf
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(T)Tj
/F24 1 Tf
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()Tj
/F6 1 Tf
9.9626 0 0 9.9626 109.431 130.962 Tm
(<)Tj
/F2 1 Tf
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-0.0003 Tc
[(0,)-380.2(and)]TJ
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(+1)Tj
/F12 1 Tf
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()Tj
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(zq)Tj
/F14 1 Tf
6.9738 0 0 6.9738 196.731 129.2251 Tm
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(T)Tj
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()Tj
/F22 1 Tf
-0.215 -0.916 TD
(2)Tj
/F6 1 Tf
9.9626 0 0 9.9626 209.205 130.962 Tm
(<)Tj
/F2 1 Tf
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-0.0001 Tc
[(0,)-380.9(since)]TJ
/F6 1 Tf
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(T)Tj
/F13 1 Tf
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(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 270.621 130.962 Tm
-0.0004 Tc
[(is)-371.1(a)]TJ
-21.0577 -1.3 TD
-0.0001 Tc
[(Salem)-306.8(t)0.3(ree)-306.4(o)0.3(f)-307(t)28.3(yp)-28.1(e)-307.3(\(i\).)-436(If)-306.1(\()]TJ
/F6 1 Tf
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( )Tj
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(\()Tj
/F6 1 Tf
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(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 190.611 121.629 Tm
()Tj
/F13 1 Tf
-0.1987 -0.8737 TD
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 193.707 118.011 Tm
(\))Tj
/F12 1 Tf
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()Tj
/F2 1 Tf
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-0.0004 Tc
(2\)\()Tj
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(\()Tj
/F6 1 Tf
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(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 238.023 121.629 Tm
()Tj
/F13 1 Tf
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(2)Tj
/F2 1 Tf
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(\))Tj
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()Tj
/F2 1 Tf
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-0.0004 Tc
(2\))Tj
/F6 1 Tf
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(<)Tj
/F2 1 Tf
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-0.0004 Tc
(1,)Tj
-21.822 -1.3 TD
-0.0001 Tc
(then)Tj
/F6 1 Tf
2.4193 0 TD
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(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 92.502 103.566 Tm
(T)Tj
/F24 1 Tf
4.9813 0 0 4.9813 98.28 105.5551 Tm
()Tj
/F6 1 Tf
9.9626 0 0 9.9626 101.475 105.0601 Tm
-0.0004 Tc
(/R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 114.021 103.566 Tm
0 Tc
(T)Tj
/F6 1 Tf
9.9626 0 0 9.9626 125.415 105.0601 Tm
(>)Tj
/F2 1 Tf
1.2918 0 TD
0.4747 Tc
[(0o)475.1(n)]TJ
/F6 1 Tf
2.506 0 TD
0 Tc
(I)Tj
/F2 1 Tf
0.5185 0 TD
0.51 Tc
[(,s)509.7(o)]TJ
/F6 1 Tf
2.1573 0 TD
0 Tc
(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 197.478 103.566 Tm
(T)Tj
/F6 1 Tf
9.9626 0 0 9.9626 208.863 105.0601 Tm
(<)Tj
/F2 1 Tf
1.2918 0 TD
0.4757 Tc
[(0o)476.1(n)]TJ
/F6 1 Tf
2.506 0 TD
0 Tc
(I)Tj
/F2 1 Tf
0.5185 0 TD
-0.0001 Tc
[(.)-869.6(S)-0.1(ince)]TJ
/F6 1 Tf
-19.1751 -1.3 TD
0 Tc
(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 68.4 90.6151 Tm
(T)Tj
/F2 1 Tf
9.9626 0 0 9.9626 74.673 92.109 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.5095 0 TD
(\))Tj
/F12 1 Tf
0.7579 0 TD
0.3686 Tc
()Tj
/F2 1 Tf
2.7571 0 TD
-0.0004 Tc
(as)Tj
/F6 1 Tf
1.2828 0 TD
0 Tc
(z)Tj
/F12 1 Tf
0.8781 0 TD
0.3686 Tc
()Tj
/F2 1 Tf
2.3687 0 TD
0 Tc
(,)Tj
/F6 1 Tf
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(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 178.11 90.6151 Tm
(T)Tj
/F2 1 Tf
9.9626 0 0 9.9626 188.244 92.109 Tm
-0.0002 Tc
[(has)-389(a)0.2(n)-388.7(o)-27.8(dd)-388.7(n)27.8(u)-0.2(m)28.2(b)-28.2(er)-389.1(of)]TJ
-12.7891 -1.3 TD
-0.0001 Tc
[(ro)-27.7(ots,)-400.8(hence)-386.8(exactly)-388.4(one,)-400.8(on)-386.8(\(1)]TJ
/F6 1 Tf
13.7179 0 TD
0 Tc
(,)Tj
/F12 1 Tf
0.4436 0 TD
()Tj
/F2 1 Tf
1 0 TD
-0.0002 Tc
[(\).)-607.7(\(On)-386.9(t)0.2(he)-387.8(other)]TJ
11.2387 41.5751 TD
[(hand,)-269(if)-253.8(\()]TJ
/F6 1 Tf
3.9379 0 TD
0 Tc
( )Tj
/F2 1 Tf
0.5574 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 379.71 496.974 Tm
()Tj
/F13 1 Tf
-0.1987 -0.8737 TD
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 382.797 493.356 Tm
(\))Tj
/F12 1 Tf
0.449 0 TD
()Tj
/F2 1 Tf
0.8383 0 TD
-0.0004 Tc
(2\)\()Tj
/F6 1 Tf
1.2765 0 TD
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( )Tj
/F2 1 Tf
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(\()Tj
/F6 1 Tf
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(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 424.971 496.974 Tm
()Tj
/F13 1 Tf
-0.1987 -0.8737 TD
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 428.085 493.356 Tm
(\))Tj
/F12 1 Tf
0.449 0 TD
()Tj
/F2 1 Tf
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(2\))Tj
/F6 1 Tf
1.1681 0 TD
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(>)Tj
/F2 1 Tf
1.0551 0 TD
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[(1,)-269.9(then)]TJ
/F6 1 Tf
3.2441 0 TD
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(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 502.947 491.862 Tm
(T)Tj
/F24 1 Tf
4.9813 0 0 4.9813 508.725 493.851 Tm
()Tj
/F6 1 Tf
9.9626 0 0 9.9626 511.911 493.356 Tm
-0.0004 Tc
(/R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 524.457 491.862 Tm
0 Tc
(T)Tj
/F6 1 Tf
9.9626 0 0 9.9626 533.502 493.356 Tm
(<)Tj
/F2 1 Tf
1.0561 0 TD
(0)Tj
-22.1002 -1.3 TD
-0.0004 Tc
(on)Tj
/F6 1 Tf
1.5041 0 TD
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(I)Tj
/F2 1 Tf
0.5185 0 TD
0.4784 Tc
[(,s)478.1(o)]TJ
/F6 1 Tf
2.0995 0 TD
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(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 372.483 478.911 Tm
(T)Tj
/F6 1 Tf
9.9626 0 0 9.9626 383.445 480.405 Tm
(>)Tj
/F2 1 Tf
1.2485 0 TD
0.4495 Tc
[(0o)449.9(n)]TJ
/F6 1 Tf
2.4545 0 TD
0 Tc
(I)Tj
/F2 1 Tf
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-0.0001 Tc
[(,)-477.5(a)0.3(nd)-450(then)]TJ
/F6 1 Tf
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(R)Tj
/F14 1 Tf
6.9738 0 0 6.9738 484.965 478.911 Tm
(T)Tj
/F2 1 Tf
9.9626 0 0 9.9626 495.72 480.405 Tm
-0.0002 Tc
[(has)-449.5(a)0.2(n)-450.1(e)-0.2(v)28(e)-0.2(n)]TJ
-17.2518 -1.3 TD
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[(n)28(u)0(m)28.4(b)-28(er)-333.7(of)-334(ro)-27.6(ots,)-332.9(a)0.4(nd)-334.3(hence)-333.4(t)28.4(w)28.4(o)0.4(,)-334.7(o)0.4(n)-334.3(\()0.4(1)]TJ
/F6 1 Tf
16.7605 0 TD
(,)Tj
/F12 1 Tf
0.4436 0 TD
()Tj
/F2 1 Tf
1 0 TD
-0.0004 Tc
(\).\))Tj
-18.2041 -1.6938 TD
-0.0002 Tc
[(The)-333.6(o)0.2(nly)-334.2(delicate)-335.4(case)-333.6(is)-333.9(if)]TJ
4.5151 -2.2675 TD
0 Tc
(\()Tj
/F6 1 Tf
0.3885 0 TD
( )Tj
/F2 1 Tf
0.5574 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 389.331 432.102 Tm
()Tj
/F13 1 Tf
-0.1987 -0.9421 TD
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 392.418 427.989 Tm
(\))Tj
/F12 1 Tf
0.6116 0 TD
()Tj
/F2 1 Tf
1 0 TD
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(2\)\()Tj
/F6 1 Tf
1.2765 0 TD
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/F2 1 Tf
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(\()Tj
/F6 1 Tf
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(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 437.823 432.102 Tm
()Tj
/F13 1 Tf
-0.1987 -0.9421 TD
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 440.919 427.989 Tm
(\))Tj
/F12 1 Tf
0.6116 0 TD
()Tj
/F2 1 Tf
1 0 TD
-0.0004 Tc
(2\))Tj
/F12 1 Tf
1.1112 0 TD
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()Tj
/F2 1 Tf
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0.2776 Tc
(1=0)Tj
/F6 1 Tf
2.3325 0 TD
0 Tc
(.)Tj
/F2 1 Tf
-17.8065 -2.2675 TD
-0.0002 Tc
[(Dene)-332.7(the)-334.5(r)-0.6(ational)-334.9(function)]TJ
/F6 1 Tf
2.5873 -2.2666 TD
0 Tc
(f)Tj
/F2 1 Tf
0.5971 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.5095 0 TD
0.2776 Tc
(\)=\()Tj
/F6 1 Tf
2.1103 0 TD
0 Tc
(z)Tj
/F2 1 Tf
0.7317 0 TD
0.2223 Tc
(+1)Tj
/F12 1 Tf
1.7228 0 TD
0 Tc
()Tj
/F6 1 Tf
1 0 TD
0.0445 Tc
(zq)Tj
/F14 1 Tf
6.9738 0 0 6.9738 429.48 379.479 Tm
0 Tc
(T)Tj
/F24 1 Tf
4.9813 0 0 4.9813 435.258 381.882 Tm
()Tj
/F22 1 Tf
-0.215 -0.916 TD
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 438.57 382.818 Tm
-0.0004 Tc
(\)\()Tj
/F6 1 Tf
0.7769 0 TD
0 Tc
(z)Tj
/F2 1 Tf
0.7317 0 TD
0.2223 Tc
(+1)Tj
/F12 1 Tf
1.7228 0 TD
0 Tc
()Tj
/F6 1 Tf
0.9991 0 TD
0.0445 Tc
(zq)Tj
/F14 1 Tf
6.9738 0 0 6.9738 490.239 379.479 Tm
0 Tc
(T)Tj
/F24 1 Tf
4.9813 0 0 4.9813 496.017 381.882 Tm
()Tj
/F22 1 Tf
-0.215 -0.916 TD
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 499.329 382.818 Tm
(\))Tj
/F12 1 Tf
0.6116 0 TD
()Tj
/F6 1 Tf
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0.0445 Tc
(z,)Tj
/F2 1 Tf
-19.2256 -2.2675 TD
-0.0001 Tc
[(so)-333(that)]TJ
/F6 1 Tf
5.7148 -1.3 TD
0 Tc
(q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 385.227 345.783 Tm
(T)Tj
/F2 1 Tf
9.9626 0 0 9.9626 394.272 347.277 Tm
0.2774 Tc
(=\()Tj
/F6 1 Tf
1.4436 0 TD
0 Tc
(z)Tj
/F2 1 Tf
0.7317 0 TD
0.2223 Tc
(+1)Tj
/F12 1 Tf
1.7218 0 TD
0 Tc
()Tj
/F6 1 Tf
1 0 TD
0.0445 Tc
(zq)Tj
/F14 1 Tf
6.9738 0 0 6.9738 452.583 345.54 Tm
0 Tc
(T)Tj
/F24 1 Tf
4.9813 0 0 4.9813 458.361 347.934 Tm
()Tj
/F22 1 Tf
-0.215 -0.916 TD
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 461.673 347.277 Tm
(\))Tj
/F6 1 Tf
0.3885 0 TD
-0.0004 Tc
(/f)Tj
/F2 1 Tf
1.0967 0 TD
0 Tc
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.5095 0 TD
(\))Tj
/F6 1 Tf
0.3885 0 TD
(.)Tj
/F2 1 Tf
-16.6059 -1.8808 TD
-0.0002 Tc
[(W)82.6(e)-379.6(need)-381.4(to)-381(iden)27.8(tify)-382.1(t)0.2(he)-381.5(sign)-381.4(of)]TJ
/F6 1 Tf
14.1696 0 TD
0 Tc
(f)Tj
/F2 1 Tf
0.5971 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.5095 0 TD
0.3808 Tc
[(\)o)381.2(n)]TJ
/F6 1 Tf
2.2061 0 TD
0 Tc
(I)Tj
/F2 1 Tf
0.5185 0 TD
-0.0002 Tc
[(.)-586.1(P)0.1(utting)]TJ
/F6 1 Tf
-18.3893 -1.3 TD
0 Tc
(x)Tj
/F2 1 Tf
0.9395 0 TD
(=)Tj
/F12 1 Tf
1.1464 0.72 TD
()Tj
ET
352.926 322.964 m
358.002 322.964 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 352.9261 315.588 Tm
(z)Tj
/F2 1 Tf
0.7679 0 TD
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-11.4205 -1.2999 TD
0 Tc
(t)Tj
/F14 1 Tf
6.9738 0 0 6.9738 86.526 622.623 Tm
(i)Tj
/F15 1 Tf
0.4039 0 TD
()Tj
/F13 1 Tf
0.8931 0 TD
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 103.356 624.1171 Tm
-0.0002 Tc
(and)Tj
/F6 1 Tf
1.945 0 TD
0 Tc
(t)Tj
/F14 1 Tf
6.9738 0 0 6.9738 126.333 622.623 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 129.645 624.1171 Tm
(.)Tj
ET
0 0 0 1 K
0 J 0 j 0.405 w 10 M []0 d
1 i
301.302 632.258 m
308.079 632.258 l
301.504 626.079 m
301.504 632.064 l
307.885 626.079 m
307.885 632.064 l
301.302 625.885 m
308.079 625.885 l
S
BT
9.9626 0 0 9.9626 74.952 600.627 Tm
-0.0003 Tc
[(Note)-321(that)-319.7(while)-320.1(in)-320.1(case)-319.2(\(i\))]TJ
/F6 1 Tf
11.7801 0 TD
0 Tc
(T)Tj
/F2 1 Tf
1.0425 0 TD
-0.0002 Tc
[(is)-319.4(a)-319.6(r)-0.6(o)-27.8(oted)-319.1(t)0.2(ree)-319.1(with)-320.9(the)]TJ
-14.0223 -1.3 TD
-0.0001 Tc
[(prop)-28.1(ert)28.3(y)-458.8(that)-458.6(remo)28.3(v)55.2(a)0.3(l)-459.5(o)0.3(f)-458.8(a)-458.6(single)-459.9(v)28.1(e)-0.1(rtex)-458.8(giv)28.1(es)-459.3(a)-458.6(f)0.1(orest)]TJ
T*
-0.0002 Tc
[(of)-364(cyclotomic)-366.1(trees,)-370.1(i)0.2(n)-364.3(c)-0.2(ase)-363.4(\(ii\))-363.8(the)-364.3(t)0.2(ree)]TJ
/F6 1 Tf
17.7072 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 245.232 573.231 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 252.108 574.725 Tm
(+)Tj
/F6 1 Tf
1.0199 0 TD
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 268.092 573.231 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 276.183 574.725 Tm
-0.0001 Tc
[(has)-363.6(t)0.3(he)]TJ
-21.3982 -1.3 TD
[(prop)-28.1(ert)28.3(y)-308(that)-308.6(remo)28.3(v)55.2(a)0.3(l)-308.6(o)0.3(f)-308.8(t)0.3(he)-308.2(edge)-308.2(j)0.1(oining)-309.5(t)0.3(he)-308.2(ro)-27.7(ots)-308.5(of)]TJ
/F6 1 Tf
23.5675 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 303.615 560.28 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 63 548.823 Tm
-0.0002 Tc
(and)Tj
/F6 1 Tf
2.0191 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 88.938 547.329 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 93.411 548.823 Tm
-0.0002 Tc
[(,)-426.2(with)-409.5(its)-409.8(inciden)27.8(t)-409(v)28(ertices,)-427.1(also)-409(giv)28(es)-408.9(a)-409(f)0(orest)-407.2(o)0.2(f)]TJ
-3.0525 -1.3 TD
[(cyclotomic)-336.3(trees.)]TJ
1.1997 -1.3 TD
[(Theorem)-378.3(7.2)-378.3(is)-378.1(a)-378.3(r)-0.6(estriction)-378.7(of)-377.6(Theorem)-378.3(3.3)-378.3(to)-378.3(trees.)]TJ
-1.1997 -1.3 TD
-0.0001 Tc
[(Ho)28.3(w)28.3(e)-0.1(v)28.1(e)-0.1(r,)-444.1(it)-421.5(is)-421.4(stronger,)-443.2(a)0.3(s)-421.4(w)28.3(e)-422(a)0.3(re)-421.1(able)-421.1(to)-421.5(sa)28.3(y)-421.8(p)-0.1(recisely)]TJ
T*
[(whic)27.9(h)-272(t)0.3(rees)-270.5(are)-271.1(S)-0.1(alem)-271.6(t)0.3(rees.)-423.3(T)0.3(heorem)-270.7(7.2)-271.6(also)-271.6(s)-0.4(ho)28.3(ws)-271.4(ho)28.3(w)]TJ
T*
[(to)-382.7(construct)-382.7(all)-383.6(Salem)-382.7(t)0.3(rees.)-591.4(T)83.4(o)-382.7(c)-0.1(onstruct)-382.7(trees)-382.6(of)-382.9(t)28.3(y)0.1(p)-28.1(e)]TJ
T*
-0.0002 Tc
[(\(i\),)-353(w)28.2(e)-348.9(tak)28(e)-349.8(a)0.2(n)27.8(y)-348.7(collection)-350.7(of)-348.7(ro)-27.8(oted)-348.9(c)-0.2(yclotomic)-350.7(trees,)-351.2(a)0.2(s)]TJ
T*
[(listed)-333.6(i)0.2(n)-332.7(Section)-332.7(6,)-333.1(the)-332.7(s)-0.5(um)-332.2(of)-332.4(whose)]TJ
/F6 1 Tf
16.3675 0 TD
0 Tc
( )Tj
/F2 1 Tf
0.5574 0 TD
-0.0001 Tc
[(-v)55.2(alues)-332.9(exceeds)-332(2.)]TJ
-16.9249 -1.3 TD
-0.0002 Tc
[(F)82.5(o)0.2(r)-316.8(t)0.2(rees)-316.7(of)-317.1(t)28.2(y)0(p)-28.2(e)-317.3(\(ii\),)-322.3(w)28.2(e)-317.3(tak)28(e)-318.2(t)28.2(w)28.2(o)-317.8(suc)27.8(h)-317.3(collections)-319.4(w)0.2(hose)]TJ
/F6 1 Tf
T*
0 Tc
( )Tj
/F2 1 Tf
0.5574 0 TD
-0.0001 Tc
[(-v)55.2(alues)-442.2(sum)-440.5(t)0.3(o)]TJ
/F6 1 Tf
6.9732 0 TD
0 Tc
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 142.695 430.7701 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 151.56 432.264 Tm
-0.0002 Tc
(and)Tj
/F6 1 Tf
2.0525 0 TD
0 Tc
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 176.679 430.7701 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 181.143 432.264 Tm
-0.0004 Tc
[(,)-468.8(with)]TJ
/F6 1 Tf
3.132 0 TD
0 Tc
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 217.017 430.7701 Tm
(1)Tj
/F18 1 Tf
9.9626 0 0 9.9626 226.035 432.264 Tm
()Tj
/F6 1 Tf
1.2349 0 TD
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 243.009 430.7701 Tm
(2)Tj
/F6 1 Tf
9.9626 0 0 9.9626 252.036 432.264 Tm
(>)Tj
/F2 1 Tf
1.2349 0 TD
-0.0001 Tc
[(2,)-468.5(sub)-55.2(j)0.1(ect)]TJ
-20.2094 -1.3 TD
-0.0002 Tc
[(to)-435.2(the)-435.6(a)0.2(dditional)-437.9(constrain)27.8(t)-437(t)0.2(hat)-435.2(\()]TJ
/F6 1 Tf
15.4325 0 TD
0 Tc
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 221.418 417.819 Tm
(1)Tj
/F12 1 Tf
9.9626 0 0 9.9626 228.78 419.313 Tm
()Tj
/F2 1 Tf
1.0678 0 TD
-0.0004 Tc
(2\)\()Tj
/F6 1 Tf
1.2765 0 TD
0 Tc
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 256.806 417.819 Tm
(2)Tj
/F12 1 Tf
9.9626 0 0 9.9626 264.177 419.313 Tm
()Tj
/F2 1 Tf
1.0678 0 TD
-0.0004 Tc
(2\))Tj
/F18 1 Tf
1.3361 0 TD
0 Tc
()Tj
/F2 1 Tf
1.225 0 TD
-0.0004 Tc
(1.)Tj
-23.822 -1.3 TD
-0.0001 Tc
[(A)-478.7(c)27.9(hec)27.9(k)-479.6(o)0.3(n)-479.8(p)-28.1(ossible)-479.8(s)-0.4(ums)-479.2(o)0.3(f)]TJ
/F6 1 Tf
13.4523 0 TD
0 Tc
( )Tj
/F2 1 Tf
0.5574 0 TD
-0.0002 Tc
[(-v)55.1(alues)-480.2(rev)28(e)-0.2(als)-480.2(that)-480.4(the)]TJ
-14.0097 -1.3 TD
-0.0001 Tc
[(smallest)-352(p)-28.1(o)0.3(ssible)-351.5(v)55.2(alue)-351.5(f)0.1(or)]TJ
/F6 1 Tf
11.7901 0 TD
0 Tc
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 185.13 391.917 Tm
(2)Tj
/F6 1 Tf
9.9626 0 0 9.9626 192.663 393.411 Tm
(>)Tj
/F2 1 Tf
1.085 0 TD
0.3514 Tc
[(2i)351.8(s8)351.8(5)]TJ
/F6 1 Tf
2.8737 0 TD
0 Tc
(/)Tj
/F2 1 Tf
0.4996 0 TD
-0.0002 Tc
[(42,)-357.5(coming)-352.1(f)0(rom)]TJ
-17.4731 -1.2999 TD
0 Tc
[(the)-337(t)0.4(ree)]TJ
/F6 1 Tf
3.7319 0 TD
(T)Tj
/F2 1 Tf
0.7236 0 TD
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
(2)Tj
/F6 1 Tf
0.4996 0 TD
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0002 Tc
[(6\),)-342.1(using)-336.7(t)0.2(he)-338.1(lab)-28.2(elling)-338.5(o)0.2(f)-337.9(F)-0.6(igure)-337.2(15.)-456.9(This)]TJ
-6.7302 -1.3 TD
-0.0001 Tc
[(implies)-304(t)0.3(he)-302.8(upp)-28.1(er)-301.3(b)-28.1(o)0.3(und)]TJ
/F6 1 Tf
10.9391 0 TD
0 Tc
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 176.652 366.015 Tm
(1)Tj
/F18 1 Tf
9.9626 0 0 9.9626 183.888 367.509 Tm
()Tj
/F2 1 Tf
1.0552 0 TD
-0.0004 Tc
[(44)-303.5(for)]TJ
/F6 1 Tf
2.8014 0 TD
0 Tc
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 226.98 366.015 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 231.453 367.509 Tm
[(.)-434.1(O)0(f)-301.5(c)0(ourse,)-308.5(when)]TJ
/F6 1 Tf
-16.9085 -1.3 TD
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 67.671 353.064 Tm
(2)Tj
/F6 1 Tf
9.9626 0 0 9.9626 74.907 354.558 Tm
(>)Tj
/F2 1 Tf
1.0552 0 TD
-0.0004 Tc
(85)Tj
/F6 1 Tf
0.9991 0 TD
0 Tc
(/)Tj
/F2 1 Tf
0.4996 0 TD
-0.0001 Tc
[(42,)-297.8(the)-286.5(upp)-28.1(er)-285.1(b)-28.1(o)0.3(und)-286.5(for)]TJ
/F6 1 Tf
10.5841 0 TD
0 Tc
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 210.465 353.064 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 217.782 354.558 Tm
-0.0002 Tc
[(will)-287(b)-28.2(e)-285.7(smaller.)-429.8(Note)]TJ
-15.5362 -1.3009 TD
[(to)-27.8(o)-334(t)0.2(hat)-334.9(t)0.2(he)-333.6(condition)]TJ
/F6 1 Tf
10.0276 0 TD
0 Tc
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 167.571 340.104 Tm
(1)Tj
/F18 1 Tf
9.9626 0 0 9.9626 174.807 341.598 Tm
()Tj
/F6 1 Tf
1.0561 0 TD
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 189.999 340.104 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 197.784 341.598 Tm
-0.0003 Tc
[(implies)-335.8(t)0.1(hat)]TJ
/F6 1 Tf
5.5612 0 TD
0 Tc
(s)Tj
/F13 1 Tf
6.9738 0 0 6.9738 257.859 340.104 Tm
(2)Tj
/F18 1 Tf
9.9626 0 0 9.9626 265.095 341.598 Tm
()Tj
/F2 1 Tf
1.0561 0 TD
-0.0004 Tc
(3.)Tj
-20.1417 -1.3 TD
-0.0001 Tc
[(The)-564.7()-0.1(rst)-564.3(e)-0.1(xamples)-565(o)0.3(f)-565.4(S)-0.1(alem)-565.2(n)27.9(um)28.3(b)-28.1(e)-0.1(rs)-564.1(of)-564.5(trace)-565.6(b)-28.1(e-)]TJ
-1.1997 -1.3 TD
-0.0004 Tc
[(lo)28(w)]TJ
/F12 1 Tf
1.9269 0 TD
0 Tc
()Tj
/F2 1 Tf
0.7778 0 TD
-0.0001 Tc
[(1)-455(w)28.3(ere)-455.4(o)0.3(btained)-456.3(using)-455(t)0.3(he)-455.4(construction)-456.3(in)-455.4(Theo-)]TJ
-2.7047 -1.3 TD
-0.0002 Tc
[(rem)-455.1(7.2\(i\))-457.8(\(see)-455.5([McKee)-455.5(and)-455.5(S)-0.2(m)28.2(y)0(th)-457.3(04]\).)-811.9(The)-456.4(s)-0.5(mallest)]TJ
T*
-0.0001 Tc
[(kno)28.3(w)0.3(n)-514.1(degree)-513.2(f)0.1(or)-513.6(a)-512.8(S)-0.1(alem)-514.6(n)27.9(um)28.3(b)-28.1(e)-0.1(r)-513.6(o)0.3(f)-513(t)0.3(race)-514.1(b)-28.1(e)-0.1(lo)28.3(w)]TJ
/F12 1 Tf
23.3227 0 TD
0 Tc
()Tj
/F2 1 Tf
0.7778 0 TD
(1)Tj
-24.1005 -1.3 TD
-0.0002 Tc
[(coming)-482.2(f)0(rom)-481.3(a)-481.3(g)0.2(raph)-480.8(is)-482(of)-481.5(degree)-480.8(460,)-519.2(obtained)-482.6(when)]TJ
/F6 1 Tf
T*
0 Tc
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 70.209 267.51 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 77.031 263.892 Tm
(=)Tj
/F12 1 Tf
1.1834 0 TD
({)Tj
/F6 1 Tf
0.4996 0 TD
(A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 101.268 262.398 Tm
-0.0003 Tc
(70)Tj
/F2 1 Tf
9.9626 0 0 9.9626 109.71 263.892 Tm
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(69\))Tj
/F6 1 Tf
1.3876 0 TD
0.1658 Tc
(,D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 149.463 262.398 Tm
-0.0003 Tc
(196)Tj
/F2 1 Tf
9.9626 0 0 9.9626 161.919 263.892 Tm
(\(182)Tj
/F6 1 Tf
1.8872 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(14\))Tj
/F6 1 Tf
1.3876 0 TD
0.1658 Tc
(,D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 211.626 262.398 Tm
-0.0003 Tc
(232)Tj
/F2 1 Tf
9.9626 0 0 9.9626 224.091 263.892 Tm
(\(220)Tj
/F6 1 Tf
1.8872 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(12\))Tj
/F12 1 Tf
1.3876 0 TD
0 Tc
(})Tj
/F2 1 Tf
0.9133 0 TD
-0.0003 Tc
[(in)-410.5(Theo-)]TJ
-20.8012 -1.3 TD
-0.0001 Tc
[(rem)-328.5(7.2\(i\).)-445.9(Muc)27.9(h)-329.9(smaller)-330.2(degrees)-329.3(ha)28.3(v)28.1(e)-329.9(b)-28.1(een)-329.9(obtained)-330.8(b)27.9(y)]TJ
T*
-0.0002 Tc
[(other)-355.6(means,)-361.1(and)-356.2(t)0.2(he)-355.2(minimal)-357.5(degree)-355.2(i)0.2(s)-355.6(k)0(no)28.2(wn)-357.1(to)-355.7(b)-28.2(e)-354.3(20)]TJ
T*
[([McKee)-440.2(and)-441.1(S)-0.2(m)28.2(y)0(th)-442(04].)-766.7(It)-440.6(is)-440.5(also)-441.5(n)-0.2(o)28.2(w)-440.6(kno)28.2(w)0.2(n)-442(t)0.2(hat)-441.5(all)]TJ
T*
-0.0001 Tc
[(in)27.9(tegers)-422.3(o)-27.7(ccur)-422.4(as)-422.3(traces)-421.4(of)-422.7(Salem)-422.5(n)27.9(um)28.3(b)-28.1(e)-0.1(rs)-421.4([McKee)-422(and)]TJ
T*
-0.0003 Tc
[(Sm)28.1(yth)-334.6(05].)]TJ
/F3 1 Tf
0 -2.6433 TD
0 Tc
[(7.1)-1200.2(Earlier)-278.6(R)0.3(esults)]TJ
/F2 1 Tf
0 -1.5999 TD
-0.0002 Tc
[(Theorem)-414.4(7.2\(i\))-416.2(generalises)-415.2([McKee)-414(et)-413.5(al.)-687.2(99,)-435.2(Corollary)]TJ
0 -1.3 TD
[(9],)-373.8(whic)27.8(h)-365.2(g)0.2(a)28.2(v)28(e)-367(t)0.2(he)-365.2(same)-365.2(construction,)-373.8(but)-364.7(only)-365.9(for)-365.6(s)-0.5(tar-)]TJ
T*
[(lik)28(e)-376(t)0.2(rees.)-568(I)-0.4(n)-374.2(1988)-376.5(Flo)28.2(y)0(d)-375.1(a)0.2(nd)-375.1(Plotnic)27.8(k)-376.7([)0.2(Flo)28.2(y)0(d)-376(a)0.2(nd)-375.1(Plot-)]TJ
T*
[(nic)27.8(k)-265.6(88,)-279.8(Theorem)-265.4(5.1],)-280.7(without)-266.3(u)-0.2(sing)-265.4(graphs)-265.2(but)-265.4(using)-265.4(a)0.2(n)]TJ
T*
-0.0001 Tc
[(unpublished)-366.9(result)-365.5(of)-367.6(Cannon,)-375.5(sho)28.3(w)28.3(e)-0.1(d)-367.8(h)-0.1(o)28.3(w)-366.5(to)-367.3(construct)]TJ
T*
-0.0002 Tc
[(Salem)-389.1(n)27.8(um)28.2(b)-28.2(e)-0.2(rs)-389(in)-389.6(a)-389.1(w)28.2(a)28.2(y)-389.4(equiv)55.1(alen)27.8(t)-390.9(to)-389.1(our)-389.1(c)-0.2(onstruction)]TJ
T*
-0.0001 Tc
[(using)-496.5(s)-0.4(tar-lik)28.1(e)-498.8(t)0.3(rees.)-933.8(T)0.3(he)-497(same)-497(construction)-498.8(w)28.3(a)0.3(s)-497.3(also)]TJ
26.4002 63.8 TD
[(published)-279.3(b)27.9(y)-278.1(Cannon)-280.2(a)0.3(nd)-279.3(W)82.7(agreic)27.9(h)-279.3([Cannon)-280.2(a)0.3(nd)-279.3(W)82.7(agre-)]TJ
0 -1.3 TD
-0.0002 Tc
[(ic)27.8(h)-406.7(92,)-425.2(Prop)-28.2(osition)-407.6(5.2])-407.2(and)-406.7(P)28.1(arry)-406.5([P)28.1(arry)-406.5(93,)-425.2(Corollary)]TJ
T*
-0.0003 Tc
[(1.8])-312.4(in)-311.1(1992.)-438.9(In)-311.1(1999)-312.4(Pirosk)55(a)-311.5(L)-0.4(ak)55(atos)-312.3([Lak)55(atos)-313.2(99,)-316(Theo-)]TJ
T*
-0.0001 Tc
[(rem)-348.4(1.2])-350.2(deduced)-348.8(essen)27.9(tially)-351.3(the)-349.7(s)-0.4(ame)-348.8(star-lik)28.1(e)-350.6(t)0.3(ree)-349.7(c)-0.1(on-)]TJ
T*
-0.0002 Tc
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[(of)-343.5(Pisot)-342.2(n)27.9(um)28.3(b)-28.3(e)0.4(rs)-342.5(\(minimal)-344(p)-28.3(o)-0.1(lynomial)]TJ
/F7 1 Tf
17.6717 0 TD
0 Tc
(z)Tj
/F8 1 Tf
5.9776 0 0 5.9776 215.982 667.3621 Tm
(2)Tj
/F10 1 Tf
8.9664 0 0 8.9664 222.183 663.5551 Tm
()Tj
/F7 1 Tf
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[(1\).)-456.5(S)-0.3(ee)-344(end)-342.6(o)-0.2(f)-342.6(S)-0.3(ection)-343.6(8.)]TJ
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-1.1997 -1.3 TD
[(their)-445(r)-0.5(o)-27.7(ots)-444.9(to)-444.1(b)-28.1(e)-443.7(the)-444.6(cen)27.9(tral)-445(v)28.1(e)-0.1(rtex.)-777.5(T)0.3(hen)-444.6(w)28.3(e)-444.6(can)-444.6(u)-0.1(se)]TJ
T*
-0.0002 Tc
[(Lemma)-374.7(7.1\(i\))-375.6(to)-373.8(compute)-375.1(t)0.2(he)-374.2(quotien)27.8(t)-375.6(of)-374(the)-374.2(l)0.2(eft)-373.8()-0.2(gure)]TJ
T*
-0.0004 Tc
[(to)-334.2(b)-28.4(e)]TJ
7.0255 -1.9142 TD
0 Tc
(1)Tj
ET
0 0 0 1 K
0.405 w
50.886 569.249 m
175.905 569.249 l
S
BT
/F6 1 Tf
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(z)Tj
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/F12 1 Tf
1.7218 0 TD
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()Tj
/F6 1 Tf
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(z)Tj
/F23 1 Tf
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/F13 1 Tf
6.9738 0 0 6.9738 99.225 560.316 Tm
(1)Tj
ET
99.162 558.89 m
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S
BT
/F14 1 Tf
6.9738 0 0 6.9738 99.162 552.963 Tm
(z)Tj
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9.9626 0 0 9.9626 106.668 556.401 Tm
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(z)Tj
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()Tj
/F13 1 Tf
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ET
117.828 558.89 m
136.008 558.89 l
S
BT
/F14 1 Tf
6.9738 0 0 6.9738 117.828 552.963 Tm
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 121.923 554.952 Tm
(2)Tj
/F15 1 Tf
6.9738 0 0 6.9738 125.802 552.963 Tm
()Tj
/F13 1 Tf
0.8931 0 TD
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 139.41 556.401 Tm
(+)Tj
/F14 1 Tf
6.9738 0 0 6.9738 150.57 560.316 Tm
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 154.665 562.314 Tm
(2)Tj
/F15 1 Tf
6.9738 0 0 6.9738 158.553 560.316 Tm
()Tj
/F13 1 Tf
0.8931 0 TD
(1)Tj
ET
150.57 558.89 m
168.75 558.89 l
S
BT
/F14 1 Tf
6.9738 0 0 6.9738 150.57 552.963 Tm
(z)Tj
/F22 1 Tf
4.9813 0 0 4.9813 154.665 554.952 Tm
(3)Tj
/F15 1 Tf
6.9738 0 0 6.9738 158.553 552.963 Tm
()Tj
/F13 1 Tf
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(1)Tj
/F23 1 Tf
9.9626 0 0 9.9626 169.947 567.453 Tm
()Tj
/F2 1 Tf
0.9946 -0.0696 TD
(=)Tj
1.1753 0.6766 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
(z)Tj
/F2 1 Tf
0.7317 0 TD
-0.0004 Tc
[(+)-222.7(1\)\()]TJ
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(2)Tj
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(z)Tj
/F2 1 Tf
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[(+1)222.7(\))]TJ
ET
191.565 569.249 m
273.24 569.249 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 204.021 559.929 Tm
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(z)Tj
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(\()Tj
/F6 1 Tf
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(z)Tj
/F13 1 Tf
6.9738 0 0 6.9738 218.043 562.8 Tm
(3)Tj
/F12 1 Tf
9.9626 0 0 9.9626 224.721 559.929 Tm
()Tj
/F6 1 Tf
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(z)Tj
/F12 1 Tf
0.7317 0 TD
()Tj
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-0.0004 Tc
(1\))Tj
/F6 1 Tf
2.2584 0.6857 TD
0 Tc
(,)Tj
/F2 1 Tf
-23.4408 -3.4852 TD
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[(so)-547.1(that)-548.9(the)-548.5(c)-0.1(orresp)-28.1(onding)-547.1(Pisot)-548.9(n)27.9(um)28.3(b)-28.1(e)-0.1(r)-547.9(h)-0.1(as)-547.9(minimal)]TJ
0 -1.3 TD
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[(p)-28.3(olynomial)]TJ
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5.302 0 TD
0 Tc
(z)Tj
/F13 1 Tf
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(3)Tj
/F12 1 Tf
9.9626 0 0 9.9626 106.389 519.087 Tm
()Tj
/F6 1 Tf
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(z)Tj
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()Tj
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[(1.)-852.5(Similarly)83.1(,)-504.7(t)0.2(he)-470(righ)27.8(t)-469.5()-0.2(gure)-469.1(has)]TJ
-9.5749 -1.3 TD
[(quotien)27.8(t)]TJ
/F14 1 Tf
6.9738 0 0 6.9738 88.56 510.06 Tm
0 Tc
(z)Tj
/F13 1 Tf
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ET
81.396 508.634 m
109.899 508.634 l
S
BT
/F14 1 Tf
6.9738 0 0 6.9738 81.396 502.698 Tm
0 Tc
(z)Tj
/F22 1 Tf
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(2)Tj
/F15 1 Tf
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()Tj
/F14 1 Tf
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(z)Tj
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()Tj
/F13 1 Tf
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/F2 1 Tf
9.9626 0 0 9.9626 111.087 506.136 Tm
-0.0004 Tc
[(,)-334.2(with)-334.7(minimal)-336(p)-28.4(olynomial)]TJ
/F6 1 Tf
11.9455 0 TD
0 Tc
(z)Tj
/F13 1 Tf
6.9738 0 0 6.9738 235.17 509.754 Tm
(2)Tj
/F12 1 Tf
9.9626 0 0 9.9626 241.848 506.136 Tm
()Tj
/F6 1 Tf
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(z)Tj
/F12 1 Tf
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()Tj
/F2 1 Tf
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-0.0004 Tc
(1.)Tj
/F3 1 Tf
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[(9.)-1201.1(SMALL)-279(ELEMENTS)-280.8(OF)-278.1(THE)-279(D)-0.1(ERIVED)-280.2(SETS)]TJ
2.0344 -1.1997 TD
-0.0002 Tc
[(OF)-278(PISO)29.7(T)-278.9(NUMBERS)]TJ
/F2 1 Tf
-2.0344 -1.8998 TD
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[(In)-359.7(this)-360.9(section,)-367.3(w)28.3(e)-360.6(giv)28.1(e)-360.6(a)-360.1(pro)-27.7(o)0.3(f)-360.3(o)0.3(f)-360.3(a)-360.1(graphical)-361(v)28.1(ersion)-360.6(of)]TJ
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[(the)-295.6(f)0(ollo)28.2(wing)-298.8(r)-0.6(esult)-295.2(o)0.2(f)-296.3(B)-0.1(ertin)-295.6([Bertin)-296.5(80].)-433.4(Recall)-296.1(that)-297(the)]TJ
0 -1.3 TD
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[(rst)-247.2(deriv)28.1(ed)-248.6(set)-248.1(o)0.3(f)-248.3(a)-248.1(giv)28.1(en)-250.4(real)-248.1(set)-247.2(i)0.3(s)-248.9(t)0.3(he)-248.5(set)-248.1(o)0.3(f)-248.3(limit)-249.9(p)-28.1(oin)27.9(ts)]TJ
T*
-0.0003 Tc
[(of)-307.2(the)-307.5(s)-0.6(et,)-312.4(w)0.1(hile)-307.5(for)]TJ
/F6 1 Tf
8.7131 0 TD
0 Tc
(k)Tj
/F18 1 Tf
0.8302 0 TD
()Tj
/F2 1 Tf
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-0.0004 Tc
[(2)-307.1(its)]TJ
/F6 1 Tf
2.1744 0 TD
0 Tc
(k)Tj
/F2 1 Tf
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[(th)-307.2(deriv)28.2(ed)-306.3(set)-306.7(i)0.4(s)-306.6(t)0.4(he)-307.2(set)-306.7(o)0.4(f)]TJ
-13.3249 -1.3 TD
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[(limit)-335.1(p)-28.4(oin)27.6(ts)-335(of)-334.4(its)-335(\()]TJ
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(k)Tj
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()Tj
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[(1\)th)-335.4(deriv)28(ed)-333.6(set.)]TJ
/F3 1 Tf
-10.0908 -2.5999 TD
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[(T)37.2(heor)11.1(em)-303.8(9.1.)]TJ
/F11 1 Tf
6.2279 0 TD
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[(Le)-51.6(t)]TJ
/F6 1 Tf
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(k)Tj
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/F11 1 Tf
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[(.T)526.3(h)526(e)526.4(n)]TJ
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(k)Tj
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(+)Tj
/F12 1 Tf
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()Tj
ET
210.69 375.749 m
237.825 375.749 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 210.69 367.239 Tm
(k)Tj
/F13 1 Tf
6.9738 0 0 6.9738 216.189 370.119 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 222.867 367.239 Tm
0.2223 Tc
[(+4)221.8(\))]TJ
/F6 1 Tf
1.889 0 TD
0 Tc
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(2)Tj
/F11 1 Tf
0.8808 0 TD
-0.0517 Tc
[(be)-51.5(l)-51.8(o)-51.9(n)-51.4(g)-51.5(s)]TJ
-21.5338 -1.3 TD
0.0002 Tc
[(to)-448.1(the)]TJ
/F2 1 Tf
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-0.0004 Tc
(\(2)Tj
/F6 1 Tf
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(k)Tj
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()Tj
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-0.0004 Tc
(1\))Tj
/F11 1 Tf
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[(th)-449.2(derive)51.7(d)-450.1(s)-0.4(et)-448.3(of)-447.7(the)-448.8(set)]TJ
/F6 1 Tf
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/F13 1 Tf
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-0.0001 Tc
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/F11 1 Tf
9.9626 0 0 9.9626 249.822 354.288 Tm
0.0001 Tc
[(of)-448.5(gr)51.4(aph)]TJ
-20.97 -1.3 TD
0 Tc
[(Pisot)-372.4(n)0.3(umb)51.7(e)0.2(rs,)-376.3(w)-0.5(hile)]TJ
/F6 1 Tf
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(k)Tj
/F2 1 Tf
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/F11 1 Tf
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[(b)51.8(e)0.3(longs)-373.3(t)-0.1(o)-372.3(the)]TJ
/F2 1 Tf
6.33 0 TD
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(\(2)Tj
/F6 1 Tf
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0 Tc
(k)Tj
/F2 1 Tf
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(\))Tj
/F11 1 Tf
0.3885 0 TD
[(th)-373.3(derive)51.7(d)]TJ
-20.3036 -1.3 TD
0.0001 Tc
[(set)-357.9(o)-0.1(f)]TJ
/F6 1 Tf
2.7345 0 TD
0 Tc
(S)Tj
/F13 1 Tf
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-0.0001 Tc
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/F11 1 Tf
9.9626 0 0 9.9626 94.608 328.386 Tm
0 Tc
(.)Tj
/F2 1 Tf
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[(Bertins)-488.3(result)-485.7(w)28.3(a)0.3(s)-488.3(t)0.3(hat)-487.5(t)0.3(hese)-486.1(n)27.9(um)28.3(b)-28.1(e)-0.1(rs)-487.4(b)-28.1(e)-0.1(longed)-487(t)0.3(o)]TJ
-1.1997 -1.3 TD
0 Tc
[(the)-404.7(c)0(orresp)-28(onding)-403.4(deriv)28.2(ed)-404.7(set)-403.4(o)0.4(f)]TJ
/F6 1 Tf
14.7062 0 TD
(S)Tj
/F2 1 Tf
0.6712 0 TD
-0.0003 Tc
[(,)-421.7(r)-0.7(ather)-405.4(than)-405(that)-405.5(of)]TJ
/F6 1 Tf
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0 Tc
(S)Tj
/F13 1 Tf
6.9738 0 0 6.9738 47.016 275.088 Tm
-0.0001 Tc
(graph)Tj
/F2 1 Tf
9.9626 0 0 9.9626 67.365 276.5821 Tm
[(.)-930.1(T)0.3(hey)-495.9(are)-495.2(t)0.3(he)-496.1(smallest)-496.5(kno)28.3(w)0.3(n)-496.1(e)-0.1(lemen)27.9(t)0.3(s)-497.3(o)0.3(f)-495.8(t)0.3(he)]TJ
-2.6559 -1.3 TD
0 Tc
[(relev)55.3(a)0.4(n)28(t)-333.8(deriv)28.2(ed)-333.4(set)-333.8(o)0.4(f)]TJ
/F6 1 Tf
9.9833 0 TD
(S)Tj
/F2 1 Tf
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(.)Tj
ET
/EmbeddedDocument /MC3 BDC
q
214.902 236.455 m
213.327 235.944 211.632 236.807 211.12 238.383 c
210.609 239.958 211.472 241.653 213.048 242.165 c
214.623 242.676 216.318 241.813 216.83 240.237 c
217.341 238.662 216.478 236.967 214.902 236.455 c
W* n
BT
/T2 1 Tf
4.8 0 0 9.6 206.2495 230.9142 Tm
0 0 0 rg
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
q
90.054 226.983 143.4 24.678 re
W n
0 0 0 RG
0.3 w
214.902 236.455 m
213.327 235.944 211.632 236.807 211.12 238.383 c
210.609 239.958 211.472 241.653 213.048 242.165 c
214.623 242.676 216.318 241.813 216.83 240.237 c
217.341 238.662 216.478 236.967 214.902 236.455 c
h
226.59 229.996 m
226.417 231.644 227.614 233.122 229.261 233.295 c
230.909 233.468 232.387 232.271 232.56 230.624 c
232.733 228.976 231.536 227.498 229.889 227.325 c
228.241 227.152 226.763 228.349 226.59 229.996 c
h
228.354 245.598 m
226.841 246.272 226.159 248.047 226.833 249.561 c
227.507 251.074 229.282 251.756 230.796 251.082 c
232.309 250.408 232.991 248.633 232.317 247.119 c
231.643 245.606 229.868 244.924 228.354 245.598 c
h
213.977 239.322 m
189.966 239.322 l
213.977 239.322 m
227.143 232.079 l
213.977 239.322 m
226.862 247.086 l
112.66 238.483 m
112.203 240.075 113.125 241.738 114.718 242.195 c
116.31 242.652 117.973 241.73 118.43 240.137 c
118.887 238.545 117.965 236.882 116.372 236.425 c
114.78 235.968 113.117 236.89 112.66 238.483 c
h
112.53 238.722 m
90.921 238.722 l
S
EMC
Q
BT
/F3 1 Tf
8.9664 0 0 8.9664 49.869 209.6851 Tm
[(FIGURE)-241.8(1)-0.1(1)]TJ
/F2 1 Tf
9.9626 0 0 9.9626 93.3922 209.6851 Tm
(.)Tj
/F9 1 Tf
8.9664 0 0 8.9664 100.3853 209.6851 Tm
-0.0002 Tc
[(The)-280.8(subtrees)-280.4(used)-281.4(t)0(o)-281.3(m)0.1(ak)28.3(e)-280.8(s)-0.3(mall)-281.8(elemen)27.8(ts)-282.4(of)]TJ
-5.634 -1.2226 TD
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[(the)-307.8(d)-0.2(eriv)28.4(ed)-307.4(sets)-308.4(of)-307.4(the)-306.8(s)-0.2(et)-308(of)-307.4(graph)-306.4(P)-0.3(isot)-307(n)27.9(u)-0.2(m)28.3(b)-28.3(ers.)-444.3(Their)]TJ
T*
[(Pisot)-305(q)0.3(uotien)27.9(ts)-304.3(are)-303.8(1)]TJ
/F7 1 Tf
9.2203 0 TD
0 Tc
(/z)Tj
/F9 1 Tf
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[(\(left\))-306.1(and)-303.5(1)]TJ
/F7 1 Tf
5.0337 0 TD
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/F9 1 Tf
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(\()Tj
/F7 1 Tf
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(z)Tj
/F10 1 Tf
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()Tj
/F9 1 Tf
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-0.0001 Tc
[(1\))-304(\(righ)27.9(t\).)-444.3(They)]TJ
-18.1305 -1.2216 TD
[(giv)28.4(e)-447.3(suc)28.1(h)-444.9(e)0.4(lemen)27.9(t)0.1(s)-447.9(a)-0.1(s)-446.9(a)-445.8(limit)-447.6(of)-445.9(increasing)-446.8(graph)-445.9(P)-0.3(isot)]TJ
0 -1.2226 TD
[(n)27.9(u)-0.2(m)28.3(b)-28.3(ers.)-456.4(See)-342.9(T)-0.6(heorem)-342.1(9.1.)]TJ
/F11 1 Tf
9.9626 0 0 9.9626 40.905 130.962 Tm
-0.0513 Tc
[(P)-51.4(roo)-51.5(f)-50.9(:)]TJ
/F2 1 Tf
3.1474 0 TD
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[(The)-363.4(p)-0.2(ro)-27.8(of)-363.1(consists)-363.7(simply)-363.2(of)-364(exhibiting)-364.7(t)28.2(w)28.2(o)-363.8(fam-)]TJ
-3.1474 -1.3 TD
[(ilies)-519.1(o)0.2(f)-519.4(t)0.2(rees)-518.2(con)27.8(taining)-520.1(2)]TJ
/F6 1 Tf
11.641 0 TD
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(k)Tj
/F2 1 Tf
0.552 0 TD
-0.0001 Tc
[(,)-565.2(r)-0.5(esp)-28.1(ectiv)28.1(ely)-518.4(2)]TJ
/F6 1 Tf
6.9796 0 TD
0 Tc
(k)Tj
/F2 1 Tf
0.898 0 TD
-0.0003 Tc
[(+)-345.4(1)-518.4(white)]TJ
-20.0705 -1.3 TD
-0.0002 Tc
[(v)28(e)-0.2(rtices,)-448.7(a)0.2(nd)-425.7(sho)28.2(wing)-426.2(t)0.2(hat)-425.3(t)0.2(heir)-426.1(r)-0.6(ecipro)-27.8(c)-0.2(al)-425.3(p)-28.2(olynomials)]TJ
T*
0 Tc
(are)Tj
/F6 1 Tf
1.777 0 TD
(z)Tj
/F13 1 Tf
6.9738 0 0 6.9738 63.684 95.727 Tm
(2)Tj
/F12 1 Tf
9.9626 0 0 9.9626 71.082 92.109 Tm
()Tj
/F6 1 Tf
1.0714 0 TD
0.0314 Tc
(kz)Tj
/F12 1 Tf
1.3551 0 TD
0 Tc
()Tj
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542.223 429.335 m
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W* n
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h
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h
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528.799 154.634 m
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317.205 140.295 215.1 65.709 re
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512.003 154.219 m
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h
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s
q
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483.893 167.298 m
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471.762 173.094 m
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228.024 616.359 226.27 616.237 225.115 617.242 c
W* n
BT
/T43 1 Tf
4.44 0 0 8.88 222.7216 615.8283 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
225.115 617.242 m
223.959 618.246 223.837 620 224.842 621.155 c
225.846 622.311 227.6 622.433 228.755 621.429 c
229.911 620.424 230.033 618.67 229.028 617.515 c
228.024 616.359 226.27 616.237 225.115 617.242 c
s
q
287.65 593.422 m
286.147 593.714 285.165 595.172 285.457 596.675 c
285.749 598.178 287.206 599.161 288.71 598.868 c
290.213 598.576 291.195 597.119 290.903 595.615 c
290.611 594.112 289.154 593.13 287.65 593.422 c
W* n
BT
/T44 1 Tf
4.44 0 0 8.88 283.0681 587.2045 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
287.65 593.422 m
286.147 593.714 285.165 595.172 285.457 596.675 c
285.749 598.178 287.206 599.161 288.71 598.868 c
290.213 598.576 291.195 597.119 290.903 595.615 c
290.611 594.112 289.154 593.13 287.65 593.422 c
s
q
279.52 578.872 m
278.017 579.164 277.035 580.621 277.327 582.125 c
277.619 583.628 279.076 584.61 280.58 584.318 c
282.083 584.026 283.065 582.569 282.773 581.065 c
282.481 579.562 281.024 578.58 279.52 578.872 c
W* n
BT
/T45 1 Tf
4.44 0 0 8.88 275.6712 575.8156 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
279.52 578.872 m
278.017 579.164 277.035 580.621 277.327 582.125 c
277.619 583.628 279.076 584.61 280.58 584.318 c
282.083 584.026 283.065 582.569 282.773 581.065 c
282.481 579.562 281.024 578.58 279.52 578.872 c
s
q
269.257 595.177 m
269.07 596.697 270.152 598.082 271.672 598.268 c
273.192 598.455 274.577 597.373 274.763 595.853 c
274.95 594.333 273.868 592.948 272.348 592.762 c
270.828 592.575 269.443 593.657 269.257 595.177 c
W* n
BT
/T46 1 Tf
4.44 0 0 8.88 268.4963 585.9487 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
0.277 w
269.257 595.177 m
269.07 596.697 270.152 598.082 271.672 598.268 c
273.192 598.455 274.577 597.373 274.763 595.853 c
274.95 594.333 273.868 592.948 272.348 592.762 c
270.828 592.575 269.443 593.657 269.257 595.177 c
s
0.277 w
259.819 602.651 m
259.22 601.241 257.59 600.583 256.181 601.181 c
254.771 601.78 254.113 603.41 254.711 604.819 c
255.31 606.229 256.94 606.887 258.349 606.289 c
259.759 605.69 260.417 604.061 259.819 602.651 c
h
245.254 610.721 m
244.655 609.311 243.025 608.653 241.616 609.251 c
240.206 609.85 239.548 611.48 240.146 612.889 c
240.745 614.299 242.375 614.957 243.784 614.359 c
245.194 613.76 245.852 612.13 245.254 610.721 c
h
272.024 595.526 m
279.422 583.764 l
272.024 595.526 m
285.895 596.081 l
269.62 596.895 m
259.929 602.295 l
255.046 604.995 m
245.318 610.358 l
S
240.325 613.207 m
226.935 619.347 l
B*
q
224.381 618.251 m
223.783 619.66 224.441 621.29 225.851 621.889 c
227.26 622.487 228.89 621.829 229.489 620.419 c
230.087 619.01 229.429 617.38 228.019 616.781 c
226.61 616.183 224.98 616.841 224.381 618.251 c
W* n
BT
/T47 1 Tf
4.44 0 0 8.88 222.7215 615.8283 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
224.381 618.251 m
223.783 619.66 224.441 621.29 225.851 621.889 c
227.26 622.487 228.89 621.829 229.489 620.419 c
230.087 619.01 229.429 617.38 228.019 616.781 c
226.61 616.183 224.98 616.841 224.381 618.251 c
s
q
227.406 554.288 m
227.593 555.808 228.978 556.89 230.498 556.703 c
232.018 556.517 233.1 555.132 232.913 553.612 c
232.727 552.092 231.342 551.01 229.822 551.197 c
228.302 551.383 227.22 552.768 227.406 554.288 c
W* n
BT
/T48 1 Tf
4.44 0 0 8.88 224.7176 547.1945 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
0.277 w
227.406 554.288 m
227.593 555.808 228.978 556.89 230.498 556.703 c
232.018 556.517 233.1 555.132 232.913 553.612 c
232.727 552.092 231.342 551.01 229.822 551.197 c
228.302 551.383 227.22 552.768 227.406 554.288 c
s
q
243.757 557.513 m
243.943 559.033 245.328 560.115 246.848 559.929 c
248.368 559.742 249.45 558.357 249.264 556.837 c
249.077 555.317 247.692 554.235 246.172 554.422 c
244.652 554.608 243.57 555.993 243.757 557.513 c
W* n
BT
/T49 1 Tf
4.44 0 0 8.88 239.6519 553.6304 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
243.757 557.513 m
243.943 559.033 245.328 560.115 246.848 559.929 c
248.368 559.742 249.45 558.357 249.264 556.837 c
249.077 555.317 247.692 554.235 246.172 554.422 c
244.652 554.608 243.57 555.993 243.757 557.513 c
s
q
234.478 566.631 m
233.09 567.278 232.489 568.929 233.136 570.317 c
233.783 571.705 235.434 572.306 236.822 571.659 c
238.21 571.012 238.811 569.361 238.164 567.973 c
237.517 566.585 235.866 565.984 234.478 566.631 c
W* n
BT
/T50 1 Tf
4.44 0 0 8.88 231.2984 559.8391 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
0.277 w
234.478 566.631 m
233.09 567.278 232.489 568.929 233.136 570.317 c
233.783 571.705 235.434 572.306 236.822 571.659 c
238.21 571.012 238.811 569.361 238.164 567.973 c
237.517 566.585 235.866 565.984 234.478 566.631 c
h
232.228 588.499 m
233.754 588.632 235.1 587.502 235.234 585.977 c
235.367 584.451 234.237 583.105 232.712 582.971 c
231.186 582.838 229.84 583.968 229.706 585.493 c
229.573 587.019 230.703 588.365 232.228 588.499 c
h
229.048 604.849 m
230.574 604.982 231.92 603.852 232.054 602.327 c
232.187 600.801 231.057 599.455 229.532 599.321 c
228.006 599.188 226.66 600.318 226.526 601.843 c
226.393 603.369 227.523 604.715 229.048 604.849 c
h
235.664 569.153 m
244.578 558.463 l
235.664 569.153 m
230.893 556.096 l
235.183 571.89 m
233.038 582.802 l
231.965 588.239 m
229.857 599.151 l
S
228.673 604.699 m
226.935 619.347 l
B*
q
211.277 638.192 m
211.75 639.649 213.316 640.447 214.772 639.973 c
216.229 639.5 217.027 637.934 216.553 636.478 c
216.08 635.021 214.514 634.223 213.058 634.697 c
211.601 635.17 210.803 636.736 211.277 638.192 c
W* n
BT
/T51 1 Tf
4.44 0 0 8.88 209.9997 634.0213 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
211.277 638.192 m
211.75 639.649 213.316 640.447 214.772 639.973 c
216.229 639.5 217.027 637.934 216.553 636.478 c
216.08 635.021 214.514 634.223 213.058 634.697 c
211.601 635.17 210.803 636.736 211.277 638.192 c
h
226.935 619.347 m
213.915 637.323 l
S
q
198.296 620.479 m
198.895 621.889 200.525 622.547 201.934 621.949 c
203.344 621.35 204.002 619.72 203.404 618.311 c
202.805 616.901 201.175 616.243 199.766 616.841 c
198.356 617.44 197.698 619.07 198.296 620.479 c
W* n
BT
/T52 1 Tf
4.44 0 0 8.88 197.2075 615.9041 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
198.296 620.479 m
198.895 621.889 200.525 622.547 201.934 621.949 c
203.344 621.35 204.002 619.72 203.404 618.311 c
202.805 616.901 201.175 616.243 199.766 616.841 c
198.356 617.44 197.698 619.07 198.296 620.479 c
s
q
194.947 553.612 m
194.76 555.132 195.842 556.517 197.362 556.703 c
198.882 556.89 200.267 555.808 200.453 554.288 c
200.64 552.768 199.558 551.383 198.038 551.197 c
196.518 551.01 195.133 552.092 194.947 553.612 c
W* n
BT
/T53 1 Tf
4.44 0 0 8.88 190.9176 547.1945 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
194.947 553.612 m
194.76 555.132 195.842 556.517 197.362 556.703 c
198.882 556.89 200.267 555.808 200.453 554.288 c
200.64 552.768 199.558 551.383 198.038 551.197 c
196.518 551.01 195.133 552.092 194.947 553.612 c
s
q
178.566 556.867 m
178.38 558.387 179.462 559.772 180.982 559.958 c
182.502 560.145 183.887 559.063 184.073 557.543 c
184.26 556.023 183.178 554.638 181.658 554.452 c
180.138 554.265 178.753 555.347 178.566 556.867 c
W* n
BT
/T54 1 Tf
4.44 0 0 8.88 175.9074 553.7063 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
178.566 556.867 m
178.38 558.387 179.462 559.772 180.982 559.958 c
182.502 560.145 183.887 559.063 184.073 557.543 c
184.26 556.023 183.178 554.638 181.658 554.452 c
180.138 554.265 178.753 555.347 178.566 556.867 c
s
q
190.948 571.659 m
192.336 572.306 193.987 571.705 194.634 570.317 c
195.281 568.929 194.68 567.278 193.292 566.631 c
191.904 565.984 190.253 566.585 189.606 567.973 c
188.959 569.361 189.56 571.012 190.948 571.659 c
W* n
BT
/T55 1 Tf
4.44 0 0 8.88 188.6251 559.8391 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
190.948 571.659 m
192.336 572.306 193.987 571.705 194.634 570.317 c
195.281 568.929 194.68 567.278 193.292 566.631 c
191.904 565.984 190.253 566.585 189.606 567.973 c
188.959 569.361 189.56 571.012 190.948 571.659 c
h
195.148 582.971 m
193.623 583.105 192.493 584.451 192.626 585.977 c
192.76 587.502 194.106 588.632 195.632 588.499 c
197.157 588.365 198.287 587.019 198.154 585.493 c
198.02 583.968 196.674 582.838 195.148 582.971 c
h
198.298 599.321 m
196.773 599.455 195.643 600.801 195.776 602.327 c
195.91 603.852 197.256 604.982 198.782 604.849 c
200.307 604.715 201.437 603.369 201.304 601.843 c
201.17 600.318 199.824 599.188 198.298 599.321 c
h
192.128 569.153 m
183.214 558.463 l
192.128 569.153 m
196.937 556.133 l
192.683 571.853 m
194.829 582.728 l
195.864 588.202 m
197.973 599.114 l
S
199.156 604.736 m
200.858 619.384 l
B*
q
199.03 621.489 m
200.186 622.493 201.939 622.371 202.944 621.215 c
203.948 620.059 203.826 618.306 202.67 617.301 c
201.514 616.297 199.761 616.419 198.756 617.575 c
197.752 618.731 197.874 620.484 199.03 621.489 c
W* n
BT
/T56 1 Tf
4.44 0 0 8.88 197.2075 615.9041 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
0.277 w
199.03 621.489 m
200.186 622.493 201.939 622.371 202.944 621.215 c
203.948 620.059 203.826 618.306 202.67 617.301 c
201.514 616.297 199.761 616.419 198.756 617.575 c
197.752 618.731 197.874 620.484 199.03 621.489 c
s
q
139.121 598.838 m
140.624 599.13 142.081 598.148 142.373 596.644 c
142.665 595.141 141.683 593.684 140.179 593.392 c
138.676 593.1 137.219 594.082 136.927 595.586 c
136.635 597.089 137.617 598.546 139.121 598.838 c
W* n
BT
/T57 1 Tf
4.44 0 0 8.88 132.4912 587.1287 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
139.121 598.838 m
140.624 599.13 142.081 598.148 142.373 596.644 c
142.665 595.141 141.683 593.684 140.179 593.392 c
138.676 593.1 137.219 594.082 136.927 595.586 c
136.635 597.089 137.617 598.546 139.121 598.838 c
s
q
147.221 584.258 m
148.724 584.55 150.181 583.568 150.473 582.064 c
150.765 580.561 149.783 579.104 148.279 578.812 c
146.776 578.52 145.319 579.502 145.027 581.006 c
144.735 582.509 145.717 583.966 147.221 584.258 c
W* n
BT
/T58 1 Tf
4.44 0 0 8.88 144.2523 575.7453 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
147.221 584.258 m
148.724 584.55 150.181 583.568 150.473 582.064 c
150.765 580.561 149.783 579.104 148.279 578.812 c
146.776 578.52 145.319 579.502 145.027 581.006 c
144.735 582.509 145.717 583.966 147.221 584.258 c
s
q
153.052 595.913 m
153.238 597.433 154.623 598.515 156.143 598.328 c
157.663 598.142 158.745 596.757 158.558 595.237 c
158.372 593.717 156.987 592.635 155.467 592.822 c
153.947 593.008 152.865 594.393 153.052 595.913 c
W* n
BT
/T59 1 Tf
4.44 0 0 8.88 151.503 586.019 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
0.277 w
153.052 595.913 m
153.238 597.433 154.623 598.515 156.143 598.328 c
157.663 598.142 158.745 596.757 158.558 595.237 c
158.372 593.717 156.987 592.635 155.467 592.822 c
153.947 593.008 152.865 594.393 153.052 595.913 c
h
173.104 604.789 m
173.702 603.379 173.044 601.75 171.634 601.151 c
170.224 600.553 168.595 601.211 167.996 602.621 c
167.398 604.031 168.056 605.66 169.466 606.259 c
170.876 606.857 172.505 606.199 173.104 604.789 c
h
187.684 612.889 m
188.282 611.479 187.624 609.85 186.214 609.251 c
184.804 608.653 183.175 609.312 182.576 610.721 c
181.978 612.131 182.636 613.76 184.046 614.359 c
185.456 614.957 187.085 614.299 187.684 612.889 c
h
155.805 595.563 m
148.408 583.801 l
155.805 595.563 m
141.898 596.081 l
158.247 596.858 m
167.975 602.295 l
172.82 604.995 m
182.548 610.358 l
S
187.431 613.207 m
200.858 619.384 l
B*
q
213.915 640.109 m
215.446 640.109 216.689 638.866 216.689 637.335 c
216.689 635.804 215.446 634.561 213.915 634.561 c
212.384 634.561 211.141 635.804 211.141 637.335 c
211.141 638.866 212.384 640.109 213.915 640.109 c
W* n
BT
/T60 1 Tf
4.44 0 0 8.88 209.9997 634.0213 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
213.915 640.109 m
215.446 640.109 216.689 638.866 216.689 637.335 c
216.689 635.804 215.446 634.561 213.915 634.561 c
212.384 634.561 211.141 635.804 211.141 637.335 c
211.141 638.866 212.384 640.109 213.915 640.109 c
h
200.858 619.384 m
213.915 637.323 l
S
q
193.082 646.969 m
194.607 646.835 195.737 645.489 195.604 643.963 c
195.47 642.438 194.124 641.308 192.598 641.441 c
191.073 641.575 189.943 642.921 190.076 644.447 c
190.21 645.972 191.556 647.102 193.082 646.969 c
W* n
BT
/T61 1 Tf
4.44 0 0 8.88 185.5926 638.9011 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
193.082 646.969 m
194.607 646.835 195.737 645.489 195.604 643.963 c
195.47 642.438 194.124 641.308 192.598 641.441 c
191.073 641.575 189.943 642.921 190.076 644.447 c
190.21 645.972 191.556 647.102 193.082 646.969 c
s
q
128.458 629.469 m
129.846 630.116 131.497 629.515 132.144 628.127 c
132.791 626.739 132.19 625.088 130.802 624.441 c
129.414 623.794 127.763 624.395 127.116 625.783 c
126.469 627.171 127.07 628.822 128.458 629.469 c
W* n
BT
/T62 1 Tf
4.44 0 0 8.88 125.7671 622.1858 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
128.458 629.469 m
129.846 630.116 131.497 629.515 132.144 628.127 c
132.791 626.739 132.19 625.088 130.802 624.441 c
129.414 623.794 127.763 624.395 127.116 625.783 c
126.469 627.171 127.07 628.822 128.458 629.469 c
s
q
126.478 646.089 m
127.866 646.736 129.517 646.135 130.164 644.747 c
130.811 643.359 130.21 641.708 128.822 641.061 c
127.434 640.414 125.783 641.015 125.136 642.403 c
124.489 643.791 125.09 645.442 126.478 646.089 c
W* n
124.587 545.961 381.6 178.779 re
W n
BT
/T63 1 Tf
4.44 0 0 8.88 121.8426 637.6453 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
q
124.587 545.961 381.6 178.779 re
W n
126.478 646.089 m
127.866 646.736 129.517 646.135 130.164 644.747 c
130.811 643.359 130.21 641.708 128.822 641.061 c
127.434 640.414 125.783 641.015 125.136 642.403 c
124.489 643.791 125.09 645.442 126.478 646.089 c
s
Q
q
144.379 638.882 m
145.423 637.762 145.362 636.005 144.242 634.961 c
143.122 633.917 141.365 633.978 140.321 635.098 c
139.277 636.218 139.338 637.975 140.458 639.019 c
141.578 640.063 143.335 640.002 144.379 638.882 c
W* n
BT
/T64 1 Tf
4.44 0 0 8.88 137.8934 633.3555 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
144.379 638.882 m
145.423 637.762 145.362 636.005 144.242 634.961 c
143.122 633.917 141.365 633.978 140.321 635.098 c
139.277 636.218 139.338 637.975 140.458 639.019 c
141.578 640.063 143.335 640.002 144.379 638.882 c
h
156.387 638.361 m
156.042 639.853 156.974 641.344 158.466 641.688 c
159.958 642.033 161.449 641.101 161.793 639.609 c
162.138 638.117 161.206 636.626 159.714 636.282 c
158.222 635.938 156.731 636.869 156.387 638.361 c
h
172.917 640.431 m
172.572 641.923 173.504 643.414 174.996 643.758 c
176.488 644.103 177.979 643.171 178.323 641.679 c
178.668 640.187 177.736 638.696 176.244 638.352 c
174.752 638.008 173.261 638.939 172.917 640.431 c
h
142.342 636.99 m
129.433 642.169 l
142.342 636.99 m
131.467 628.372 l
145.079 637.286 m
156.101 638.618 l
161.613 639.321 m
172.635 640.689 l
S
178.369 641.281 m
192.831 644.203 l
B*
q
194.269 646.583 m
195.581 645.794 196.007 644.089 195.218 642.776 c
194.429 641.464 192.724 641.038 191.411 641.827 c
190.099 642.616 189.673 644.321 190.462 645.634 c
191.251 646.946 192.956 647.372 194.269 646.583 c
W* n
BT
/T65 1 Tf
4.44 0 0 8.88 185.5925 638.9011 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
0.277 w
194.269 646.583 m
195.581 645.794 196.007 644.089 195.218 642.776 c
194.429 641.464 192.724 641.038 191.411 641.827 c
190.099 642.616 189.673 644.321 190.462 645.634 c
191.251 646.946 192.956 647.372 194.269 646.583 c
s
q
154.196 696.55 m
154.939 695.211 154.454 693.521 153.115 692.779 c
151.776 692.036 150.086 692.521 149.344 693.86 c
148.601 695.199 149.086 696.889 150.425 697.631 c
151.764 698.374 153.454 697.889 154.196 696.55 c
W* n
BT
/T66 1 Tf
4.44 0 0 8.88 147.8777 687.634 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
0.277 w
154.196 696.55 m
154.939 695.211 154.454 693.521 153.115 692.779 c
151.776 692.036 150.086 692.521 149.344 693.86 c
148.601 695.199 149.086 696.889 150.425 697.631 c
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s
q
142.856 684.34 m
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137.261 682.989 137.746 684.679 139.085 685.421 c
140.424 686.164 142.114 685.679 142.856 684.34 c
W* n
BT
/T67 1 Tf
4.44 0 0 8.88 134.0448 672.1015 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
142.856 684.34 m
143.599 683.001 143.114 681.311 141.775 680.569 c
140.436 679.826 138.746 680.311 138.004 681.65 c
137.261 682.989 137.746 684.679 139.085 685.421 c
140.424 686.164 142.114 685.679 142.856 684.34 c
s
q
155.711 682.388 m
157.214 682.68 158.671 681.698 158.963 680.194 c
159.255 678.691 158.273 677.234 156.769 676.942 c
155.266 676.65 153.809 677.632 153.517 679.136 c
153.225 680.639 154.207 682.096 155.711 682.388 c
W* n
BT
/T68 1 Tf
4.44 0 0 8.88 152.3908 674.3235 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
0.277 w
155.711 682.388 m
157.214 682.68 158.671 681.698 158.963 680.194 c
159.255 678.691 158.273 677.234 156.769 676.942 c
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s
0.277 w
170.36 666.081 m
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167.876 671.273 169.629 671.151 170.634 669.995 c
171.638 668.839 171.516 667.086 170.36 666.081 c
h
182.555 654.711 m
181.399 653.707 179.646 653.829 178.641 654.985 c
177.637 656.141 177.759 657.894 178.915 658.899 c
180.071 659.903 181.824 659.781 182.829 658.625 c
183.833 657.469 183.711 655.716 182.555 654.711 c
s
0.277 w
156.249 679.675 m
142.785 683.078 l
156.249 679.675 m
152.439 693.065 l
158.21 677.752 m
166.421 670.206 l
170.453 666.433 m
178.59 658.814 l
S
182.807 655.041 m
192.831 644.203 l
B*
q
216.553 638.192 m
217.027 636.736 216.229 635.17 214.772 634.697 c
213.316 634.223 211.75 635.021 211.277 636.478 c
210.803 637.934 211.601 639.5 213.058 639.973 c
214.514 640.447 216.08 639.649 216.553 638.192 c
W* n
BT
/T69 1 Tf
4.44 0 0 8.88 209.9997 634.0213 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
0.277 w
216.553 638.192 m
217.027 636.736 216.229 635.17 214.772 634.697 c
213.316 634.223 211.75 635.021 211.277 636.478 c
210.803 637.934 211.601 639.5 213.058 639.973 c
214.514 640.447 216.08 639.649 216.553 638.192 c
s
0.277 w
192.831 644.203 m
213.915 637.323 l
S
q
400.308 549.142 m
400.361 550.672 401.646 551.871 403.177 551.818 c
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405.799 547.418 404.514 546.219 402.983 546.273 c
401.453 546.326 400.254 547.611 400.308 549.142 c
W* n
BT
/T70 1 Tf
4.44 0 0 8.88 397.3981 537.3591 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
q
124.587 545.961 381.6 178.779 re
W n
400.308 549.142 m
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s
Q
q
384.618 554.812 m
384.671 556.342 385.956 557.541 387.487 557.487 c
389.017 557.434 390.216 556.149 390.162 554.618 c
390.109 553.088 388.824 551.889 387.293 551.943 c
385.763 551.996 384.564 553.281 384.618 554.812 c
W* n
BT
/T71 1 Tf
4.44 0 0 8.88 383.7955 548.748 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
384.618 554.812 m
384.671 556.342 385.956 557.541 387.487 557.487 c
389.017 557.434 390.216 556.149 390.162 554.618 c
390.109 553.088 388.824 551.889 387.293 551.943 c
385.763 551.996 384.564 553.281 384.618 554.812 c
s
q
399.165 567.567 m
400.637 567.989 402.174 567.137 402.597 565.665 c
403.019 564.193 402.167 562.656 400.695 562.233 c
399.223 561.811 397.686 562.663 397.263 564.135 c
396.841 565.607 397.693 567.145 399.165 567.567 c
W* n
BT
/T72 1 Tf
4.44 0 0 8.88 395.5538 560.2155 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
399.165 567.567 m
400.637 567.989 402.174 567.137 402.597 565.665 c
403.019 564.193 402.167 562.656 400.695 562.233 c
399.223 561.811 397.686 562.663 397.263 564.135 c
396.841 565.607 397.693 567.145 399.165 567.567 c
h
410.719 593.693 m
409.233 594.064 408.328 595.57 408.698 597.056 c
409.069 598.542 410.575 599.447 412.061 599.077 c
413.547 598.706 414.452 597.2 414.082 595.714 c
413.711 594.228 412.205 593.323 410.719 593.693 c
h
405.019 578.063 m
403.533 578.434 402.628 579.94 402.998 581.426 c
403.369 582.912 404.875 583.817 406.361 583.447 c
407.847 583.076 408.752 581.57 408.382 580.084 c
408.011 578.598 406.505 577.693 405.019 578.063 c
h
399.931 564.899 m
389.537 555.726 l
399.931 564.899 m
402.631 551.287 l
400.966 567.489 m
404.702 577.919 l
406.626 583.135 m
410.436 593.566 l
S
q
429.228 548.948 m
429.174 550.479 430.373 551.764 431.903 551.818 c
433.434 551.871 434.719 550.672 434.772 549.142 c
434.826 547.611 433.627 546.326 432.097 546.273 c
430.566 546.219 429.281 547.418 429.228 548.948 c
W* n
BT
/T73 1 Tf
4.44 0 0 8.88 428.6122 537.3591 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
q
124.587 545.961 381.6 178.779 re
W n
429.228 548.948 m
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s
Q
q
444.918 554.618 m
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449.124 557.541 450.409 556.342 450.462 554.812 c
450.516 553.281 449.317 551.996 447.787 551.943 c
446.256 551.889 444.971 553.088 444.918 554.618 c
W* n
BT
/T74 1 Tf
4.44 0 0 8.88 442.2148 548.748 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
444.918 554.618 m
444.864 556.149 446.063 557.434 447.593 557.487 c
449.124 557.541 450.409 556.342 450.462 554.812 c
450.516 553.281 449.317 551.996 447.787 551.943 c
446.256 551.889 444.971 553.088 444.918 554.618 c
s
q
434.385 562.233 m
432.913 562.656 432.061 564.193 432.483 565.665 c
432.906 567.137 434.443 567.989 435.915 567.567 c
437.387 567.145 438.239 565.607 437.817 564.135 c
437.394 562.663 435.857 561.811 434.385 562.233 c
W* n
BT
/T75 1 Tf
4.44 0 0 8.88 430.4565 560.2155 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
434.385 562.233 m
432.913 562.656 432.061 564.193 432.483 565.665 c
432.906 567.137 434.443 567.989 435.915 567.567 c
437.387 567.145 438.239 565.607 437.817 564.135 c
437.394 562.663 435.857 561.811 434.385 562.233 c
h
423.019 599.077 m
424.505 599.447 426.011 598.542 426.382 597.056 c
426.752 595.57 425.847 594.064 424.361 593.693 c
422.875 593.323 421.369 594.228 420.998 595.714 c
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h
428.689 583.447 m
430.175 583.817 431.681 582.912 432.052 581.426 c
432.422 579.94 431.517 578.434 430.031 578.063 c
428.545 577.693 427.039 578.598 426.668 580.084 c
426.298 581.57 427.203 583.076 428.689 583.447 c
h
435.144 564.899 m
445.538 555.726 l
435.144 564.899 m
432.444 551.287 l
434.108 567.489 m
430.372 577.919 l
428.449 583.135 m
424.639 593.566 l
S
q
415.796 611.261 m
415.198 612.671 415.857 614.3 417.266 614.899 c
418.676 615.497 420.305 614.839 420.904 613.429 c
421.502 612.019 420.844 610.39 419.434 609.791 c
418.024 609.193 416.395 609.852 415.796 611.261 c
W* n
BT
/T76 1 Tf
4.44 0 0 8.88 414.6345 601.8466 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
415.796 611.261 m
415.198 612.671 415.857 614.3 417.266 614.899 c
418.676 615.497 420.305 614.839 420.904 613.429 c
421.502 612.019 420.844 610.39 419.434 609.791 c
418.024 609.193 416.395 609.852 415.796 611.261 c
s
412.544 598.485 m
418.092 611.801 l
B*
422.531 599.04 m
418.092 611.801 l
B*
q
483.645 576.722 m
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483.574 581.844 485.286 582.239 486.585 581.428 c
487.884 580.616 488.279 578.904 487.468 577.605 c
486.656 576.306 484.944 575.911 483.645 576.722 c
W* n
BT
/T77 1 Tf
4.44 0 0 8.88 481.5618 570.7869 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
0.277 w
483.645 576.722 m
482.346 577.534 481.951 579.246 482.762 580.545 c
483.574 581.844 485.286 582.239 486.585 581.428 c
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486.656 576.306 484.944 575.911 483.645 576.722 c
s
q
470.88 565.982 m
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475.119 569.876 475.514 568.164 474.703 566.865 c
473.891 565.566 472.179 565.171 470.88 565.982 c
W* n
BT
/T78 1 Tf
4.44 0 0 8.88 464.9196 558.2153 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
470.88 565.982 m
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s
q
467.108 584.966 m
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472.121 582.138 470.615 581.233 469.129 581.603 c
467.643 581.974 466.738 583.48 467.108 584.966 c
W* n
BT
/T79 1 Tf
4.44 0 0 8.88 464.2552 581.2178 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
0.277 w
467.108 584.966 m
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472.121 582.138 470.615 581.233 469.129 581.603 c
467.643 581.974 466.738 583.48 467.108 584.966 c
h
450.271 608.018 m
449.207 606.916 447.45 606.886 446.348 607.949 c
445.246 609.013 445.216 610.77 446.279 611.872 c
447.343 612.974 449.1 613.004 450.202 611.941 c
451.304 610.877 451.334 609.12 450.271 608.018 c
h
460.966 595.268 m
459.902 594.166 458.145 594.136 457.043 595.199 c
455.941 596.263 455.911 598.02 456.974 599.122 c
458.038 600.224 459.795 600.254 460.897 599.191 c
461.999 598.127 462.029 596.37 460.966 595.268 c
h
469.802 584.281 m
472.54 570.669 l
469.802 584.281 m
482.933 579.806 l
468.101 586.464 m
460.925 594.897 l
457.374 599.188 m
450.235 607.695 l
S
q
498.288 601.646 m
496.936 602.365 496.422 604.045 497.141 605.397 c
497.859 606.75 499.54 607.263 500.892 606.544 c
502.244 605.826 502.758 604.145 502.039 602.793 c
501.32 601.441 499.64 600.927 498.288 601.646 c
W* n
BT
/T80 1 Tf
4.44 0 0 8.88 492.7288 594.2278 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
498.288 601.646 m
496.936 602.365 496.422 604.045 497.141 605.397 c
497.859 606.75 499.54 607.263 500.892 606.544 c
502.244 605.826 502.758 604.145 502.039 602.793 c
501.32 601.441 499.64 600.927 498.288 601.646 c
s
q
501.198 618.086 m
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505.154 622.266 505.668 620.585 504.949 619.233 c
504.231 617.881 502.55 617.367 501.198 618.086 c
W* n
BT
/T81 1 Tf
4.44 0 0 8.88 498.5694 609.3137 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
q
124.587 545.961 381.6 178.779 re
W n
501.198 618.086 m
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s
Q
q
489.337 612.764 m
488.235 611.701 486.478 611.731 485.414 612.833 c
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486.585 617.819 488.342 617.789 489.406 616.687 c
490.469 615.585 490.439 613.828 489.337 612.764 c
W* n
BT
/T82 1 Tf
4.44 0 0 8.88 481.7065 606.6533 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
489.337 612.764 m
488.235 611.701 486.478 611.731 485.414 612.833 c
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486.585 617.819 488.342 617.789 489.406 616.687 c
490.469 615.585 490.439 613.828 489.337 612.764 c
h
451.743 621.33 m
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456.655 618.328 455.117 617.476 453.645 617.898 c
452.173 618.32 451.321 619.858 451.743 621.33 c
h
468.123 618.48 m
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473.027 619.96 473.879 618.422 473.457 616.95 c
473.035 615.478 471.497 614.626 470.025 615.048 c
468.553 615.471 467.701 617.008 468.123 618.48 c
h
487.409 614.76 m
500.54 619.199 l
487.409 614.76 m
497.84 605.624 l
484.672 615.167 m
473.76 617.164 l
468.286 618.089 m
457.337 620.012 l
S
q
437.572 621.217 m
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435.343 625.828 436.728 626.91 438.248 626.724 c
439.768 626.537 440.85 625.152 440.663 623.632 c
440.477 622.112 439.092 621.03 437.572 621.217 c
W* n
BT
/T83 1 Tf
4.44 0 0 8.88 431.5648 616.1936 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
0.277 w
437.572 621.217 m
436.052 621.403 434.97 622.788 435.157 624.308 c
435.343 625.828 436.728 626.91 438.248 626.724 c
439.768 626.537 440.85 625.152 440.663 623.632 c
440.477 622.112 439.092 621.03 437.572 621.217 c
s
0.277 w
447.017 611.986 m
438.288 623.452 l
B*
451.53 620.9 m
438.288 623.452 l
B*
q
483.645 576.722 m
482.346 577.534 481.951 579.246 482.762 580.545 c
483.574 581.844 485.286 582.239 486.585 581.428 c
487.884 580.616 488.279 578.904 487.468 577.605 c
486.656 576.306 484.944 575.911 483.645 576.722 c
W* n
BT
/T84 1 Tf
4.44 0 0 8.88 481.5618 570.7869 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
0.277 w
483.645 576.722 m
482.346 577.534 481.951 579.246 482.762 580.545 c
483.574 581.844 485.286 582.239 486.585 581.428 c
487.884 580.616 488.279 578.904 487.468 577.605 c
486.656 576.306 484.944 575.911 483.645 576.722 c
s
q
470.88 565.982 m
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475.119 569.876 475.514 568.164 474.703 566.865 c
473.891 565.566 472.179 565.171 470.88 565.982 c
W* n
BT
/T85 1 Tf
4.44 0 0 8.88 464.9196 558.2153 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
470.88 565.982 m
469.581 566.794 469.186 568.506 469.997 569.805 c
470.809 571.104 472.521 571.499 473.82 570.688 c
475.119 569.876 475.514 568.164 474.703 566.865 c
473.891 565.566 472.179 565.171 470.88 565.982 c
s
q
467.108 584.966 m
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472.121 582.138 470.615 581.233 469.129 581.603 c
467.643 581.974 466.738 583.48 467.108 584.966 c
W* n
BT
/T86 1 Tf
4.44 0 0 8.88 464.2552 581.2178 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
0.277 w
467.108 584.966 m
467.479 586.452 468.985 587.357 470.471 586.987 c
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472.121 582.138 470.615 581.233 469.129 581.603 c
467.643 581.974 466.738 583.48 467.108 584.966 c
h
450.271 608.018 m
449.207 606.916 447.45 606.886 446.348 607.949 c
445.246 609.013 445.216 610.77 446.279 611.872 c
447.343 612.974 449.1 613.004 450.202 611.941 c
451.304 610.877 451.334 609.12 450.271 608.018 c
h
460.966 595.268 m
459.902 594.166 458.145 594.136 457.043 595.199 c
455.941 596.263 455.911 598.02 456.974 599.122 c
458.038 600.224 459.795 600.254 460.897 599.191 c
461.999 598.127 462.029 596.37 460.966 595.268 c
h
469.802 584.281 m
472.54 570.669 l
469.802 584.281 m
482.933 579.806 l
468.101 586.464 m
460.925 594.897 l
457.374 599.188 m
450.235 607.695 l
S
q
498.288 601.646 m
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502.244 605.826 502.758 604.145 502.039 602.793 c
501.32 601.441 499.64 600.927 498.288 601.646 c
W* n
BT
/T87 1 Tf
4.44 0 0 8.88 492.7288 594.2278 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
498.288 601.646 m
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q
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()Tj
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0 Tc
()Tj
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Q
489.337 612.764 m
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q
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W* n
BT
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()Tj
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()Tj
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()Tj
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ET
Q
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451.53 620.9 m
438.288 623.452 l
B*
q
483.645 576.722 m
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W* n
BT
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4.44 0 0 8.88 481.5618 570.7869 Tm
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()Tj
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ET
Q
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q
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W* n
BT
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0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
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q
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W* n
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0 Tc
()Tj
T*
()Tj
ET
Q
0.277 w
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h
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h
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h
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S
q
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W* n
BT
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()Tj
0 1 TD
()Tj
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()Tj
ET
Q
498.288 601.646 m
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s
q
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W* n
BT
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()Tj
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Q
q
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q
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W* n
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()Tj
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()Tj
ET
Q
489.337 612.764 m
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h
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h
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q
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W* n
BT
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0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
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()Tj
ET
Q
0.277 w
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B*
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q
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W* n
BT
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0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
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Q
q
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W* n
BT
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0 Tc
()Tj
T*
()Tj
ET
Q
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h
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h
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h
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S
q
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W* n
BT
/T101 1 Tf
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0 Tc
()Tj
T*
()Tj
ET
Q
487.14 687.827 m
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s
q
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W* n
BT
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0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
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s
q
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W* n
BT
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0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
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h
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q
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W* n
BT
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4.44 0 0 8.88 431.0507 635.0497 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
439.885 645.055 m
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s
452.566 648.605 m
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B*
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B*
q
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W* n
BT
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0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
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()Tj
ET
Q
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q
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W* n
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()Tj
0 1 TD
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0 -1 TD
()Tj
0 1 TD
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ET
Q
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W* n
BT
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()Tj
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0 -1 TD
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()Tj
ET
Q
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q
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W* n
BT
/T108 1 Tf
4.44 0 0 8.88 331.0608 656.0576 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
337.902 668.554 m
339.254 667.836 339.768 666.155 339.049 664.803 c
338.331 663.451 336.65 662.937 335.298 663.656 c
333.946 664.375 333.432 666.055 334.151 667.407 c
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s
q
334.992 652.114 m
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331.036 647.935 330.522 649.615 331.241 650.967 c
331.959 652.319 333.64 652.833 334.992 652.114 c
W* n
BT
/T109 1 Tf
4.44 0 0 8.88 329.6602 640.9716 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
334.992 652.114 m
336.344 651.396 336.858 649.715 336.139 648.363 c
335.421 647.011 333.74 646.497 332.388 647.216 c
331.036 647.935 330.522 649.615 331.241 650.967 c
331.959 652.319 333.64 652.833 334.992 652.114 c
s
q
346.853 657.451 m
347.955 658.514 349.712 658.484 350.776 657.382 c
351.839 656.28 351.809 654.523 350.707 653.459 c
349.605 652.396 347.848 652.426 346.784 653.528 c
345.721 654.63 345.751 656.387 346.853 657.451 c
W* n
BT
/T110 1 Tf
4.44 0 0 8.88 342.083 643.632 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
346.853 657.451 m
347.955 658.514 349.712 658.484 350.776 657.382 c
351.839 656.28 351.809 654.523 350.707 653.459 c
349.605 652.396 347.848 652.426 346.784 653.528 c
345.721 654.63 345.751 656.387 346.853 657.451 c
h
384.447 648.87 m
384.025 647.398 382.487 646.546 381.015 646.968 c
379.543 647.391 378.691 648.928 379.113 650.4 c
379.535 651.872 381.073 652.724 382.545 652.302 c
384.017 651.88 384.869 650.342 384.447 648.87 c
h
368.037 651.72 m
367.615 650.248 366.077 649.396 364.605 649.818 c
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h
348.775 655.448 m
335.644 651.009 l
348.775 655.448 m
338.345 664.584 l
351.513 655.041 m
362.424 653.043 l
367.899 652.119 m
378.847 650.195 l
S
q
398.618 648.998 m
400.138 648.812 401.22 647.427 401.033 645.907 c
400.847 644.387 399.462 643.305 397.942 643.492 c
396.422 643.678 395.34 645.063 395.527 646.583 c
395.713 648.103 397.098 649.185 398.618 648.998 c
W* n
BT
/T111 1 Tf
4.44 0 0 8.88 392.2248 642.9717 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
0.277 w
398.618 648.998 m
400.138 648.812 401.22 647.427 401.033 645.907 c
400.847 644.387 399.462 643.305 397.942 643.492 c
396.422 643.678 395.34 645.063 395.527 646.583 c
395.713 648.103 397.098 649.185 398.618 648.998 c
s
0.277 w
389.167 658.222 m
397.896 646.755 l
B*
384.654 649.307 m
397.896 646.755 l
B*
q
334.758 607.504 m
336.11 608.223 337.79 607.71 338.509 606.357 c
339.228 605.005 338.715 603.325 337.362 602.606 c
336.01 601.887 334.33 602.401 333.611 603.753 c
332.892 605.105 333.405 606.786 334.758 607.504 c
W* n
BT
/T112 1 Tf
4.44 0 0 8.88 329.9511 596.1548 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
334.758 607.504 m
336.11 608.223 337.79 607.71 338.509 606.357 c
339.228 605.005 338.715 603.325 337.362 602.606 c
336.01 601.887 334.33 602.401 333.611 603.753 c
332.892 605.105 333.405 606.786 334.758 607.504 c
s
q
331.818 623.944 m
333.17 624.663 334.85 624.15 335.569 622.797 c
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333.07 618.327 331.39 618.841 330.671 620.193 c
329.952 621.545 330.466 623.225 331.818 623.944 c
W* n
BT
/T113 1 Tf
4.44 0 0 8.88 328.5506 611.2408 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
331.818 623.944 m
333.17 624.663 334.85 624.15 335.569 622.797 c
336.288 621.445 335.775 619.765 334.422 619.046 c
333.07 618.327 331.39 618.841 330.671 620.193 c
329.952 621.545 330.466 623.225 331.818 623.944 c
s
q
350.137 617.731 m
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345.181 614.803 345.151 616.56 346.214 617.662 c
347.278 618.764 349.035 618.794 350.137 617.731 c
W* n
BT
/T114 1 Tf
4.44 0 0 8.88 340.9734 608.5804 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
350.137 617.731 m
351.239 616.667 351.269 614.91 350.206 613.808 c
349.142 612.706 347.385 612.676 346.283 613.739 c
345.181 614.803 345.151 616.56 346.214 617.662 c
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s
0.277 w
378.543 620.76 m
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h
362.163 617.91 m
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s
0.277 w
348.221 615.722 m
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348.221 615.722 m
337.79 606.586 l
350.958 616.129 m
361.869 618.126 l
367.344 619.051 m
378.292 620.974 l
S
q
349.05 582.388 m
350.349 583.199 352.061 582.804 352.873 581.505 c
353.684 580.206 353.289 578.494 351.99 577.682 c
350.691 576.871 348.979 577.266 348.167 578.565 c
347.356 579.864 347.751 581.576 349.05 582.388 c
W* n
BT
/T115 1 Tf
4.44 0 0 8.88 345.5581 572.7085 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
0.277 w
349.05 582.388 m
350.349 583.199 352.061 582.804 352.873 581.505 c
353.684 580.206 353.289 578.494 351.99 577.682 c
350.691 576.871 348.979 577.266 348.167 578.565 c
347.356 579.864 347.751 581.576 349.05 582.388 c
s
q
361.8 571.648 m
363.099 572.459 364.811 572.064 365.623 570.765 c
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363.441 566.131 361.729 566.526 360.917 567.825 c
360.106 569.124 360.501 570.836 361.8 571.648 c
W* n
BT
/T116 1 Tf
4.44 0 0 8.88 357.7603 560.1369 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
361.8 571.648 m
363.099 572.459 364.811 572.064 365.623 570.765 c
366.434 569.466 366.039 567.754 364.74 566.942 c
363.441 566.131 361.729 566.526 360.917 567.825 c
360.106 569.124 360.501 570.836 361.8 571.648 c
s
q
363.128 584.584 m
362.758 586.07 363.663 587.576 365.149 587.947 c
366.635 588.317 368.141 587.412 368.512 585.926 c
368.882 584.44 367.977 582.934 366.491 582.563 c
365.005 582.193 363.499 583.098 363.128 584.584 c
W* n
BT
/T117 1 Tf
4.44 0 0 8.88 358.4248 574.2593 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
0.277 w
363.128 584.584 m
362.758 586.07 363.663 587.576 365.149 587.947 c
366.635 588.317 368.141 587.412 368.512 585.926 c
368.882 584.44 367.977 582.934 366.491 582.563 c
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s
0.277 w
389.356 612.832 m
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h
378.661 600.082 m
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h
365.827 585.243 m
363.09 571.668 l
365.827 585.243 m
352.696 580.767 l
367.529 587.425 m
374.705 595.859 l
378.255 600.15 m
385.394 608.657 l
S
q
396.305 625.16 m
397.226 626.383 398.967 626.627 400.19 625.706 c
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399.814 620.598 398.073 620.353 396.85 621.275 c
395.627 622.196 395.383 623.937 396.305 625.16 c
W* n
BT
/T118 1 Tf
4.44 0 0 8.88 392.7389 615.2356 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
396.305 625.16 m
397.226 626.383 398.967 626.627 400.19 625.706 c
401.413 624.784 401.657 623.043 400.736 621.82 c
399.814 620.598 398.073 620.353 396.85 621.275 c
395.627 622.196 395.383 623.937 396.305 625.16 c
s
383.619 621.603 m
397.896 623.452 l
B*
389.056 613.244 m
397.896 623.452 l
B*
q
412.408 719.192 m
412.882 717.736 412.084 716.17 410.627 715.697 c
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406.658 718.934 407.456 720.5 408.913 720.973 c
410.369 721.447 411.935 720.649 412.408 719.192 c
W* n
BT
/T119 1 Tf
4.44 0 0 8.88 406.3499 707.2318 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
412.408 719.192 m
412.882 717.736 412.084 716.17 410.627 715.697 c
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s
q
429.058 719.192 m
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423.308 718.934 424.106 720.5 425.563 720.973 c
427.019 721.447 428.585 720.649 429.058 719.192 c
W* n
BT
/T120 1 Tf
4.44 0 0 8.88 421.8797 707.2318 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
429.058 719.192 m
429.532 717.736 428.734 716.17 427.277 715.697 c
425.821 715.223 424.255 716.021 423.782 717.478 c
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s
q
419.711 702.201 m
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W* n
BT
/T121 1 Tf
4.44 0 0 8.88 414.1148 697.2502 Tm
0 Tc
()Tj
0 1 TD
()Tj
0 -1 TD
()Tj
0 1 TD
()Tj
ET
Q
419.711 702.201 m
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h
417.85 662.834 m
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h
417.85 685.034 m
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s
q
420.839 635.405 m
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W* n
BT
/T122 1 Tf
4.44 0 0 8.88 414.1148 629.5826 Tm
0 Tc
()Tj
T*
()Tj
ET
Q
420.839 635.405 m
420.999 633.882 419.893 632.516 418.37 632.356 c
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h
418.092 704.458 m
424.787 716.627 l
418.092 704.458 m
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418.092 657.297 m
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418.092 635.104 l
418.092 612.911 m
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S
418.092 634.549 m
438.066 624.007 l
B*
417.537 635.104 m
436.956 646.755 l
B*
418.092 635.104 m
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B*
418.092 635.104 m
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B*
EMC
BT
8.9664 0 0 8.9664 74.952 526.9171 Tm
0 0 0 1 k
0 Tc
[(FIGURE)-297(1)-0.1(4)]TJ
/F2 1 Tf
9.9626 0 0 9.9626 118.9702 526.9171 Tm
(.)Tj
/F9 1 Tf
8.9664 0 0 8.9664 126.7103 526.9171 Tm
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(k)Tj
/F9 1 Tf
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/F10 1 Tf
1.0402 0.8171 TD
()Tj
ET
0 0 0 1 K
0.387 w
290.412 534.437 m
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S
BT
/F7 1 Tf
8.9664 0 0 8.9664 290.412 526.9171 Tm
(k)Tj
/F8 1 Tf
5.9776 0 0 5.9776 295.47 529.491 Tm
(2)Tj
/F9 1 Tf
8.9664 0 0 8.9664 301.671 526.9171 Tm
0.2285 Tc
[(+4)228.5(\))]TJ
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(k)Tj
/F10 1 Tf
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()Tj
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-38.1473 -1.2226 TD
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[(Pisot)-372.2(n)28(um)28.4(b)-28.2(e)0.5(rs)-370.5(\(left,)]TJ
/F7 1 Tf
9.3729 0 TD
(k)Tj
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[(=)-333.7(5)-371.3(sho)28.2(wn\),)-376.9(and)-371.4(t)0.3(hat)]TJ
/F7 1 Tf
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(k)Tj
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[(+)-247.6(1)-372.5(b)-28.3(e)0.4(longs)-372.6(t)0.1(o)-371.5(t)0.1(he)-371(\(2)]TJ
/F7 1 Tf
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(k)Tj
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-31.435 -1.2226 TD
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/F2 1 Tf
9.9626 0 0 9.9626 63 449.454 Tm
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0 -1.3 TD
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[(ing)-290.6(t)0.3(he)-290.1(5-)-290.1(and)-290.1(11-v)28.1(e)-0.1(rtex)-291.7(graphs)-289.5(in)-291(Figure)-289.2(13)-290.6(to)-290.6(construct)]TJ
T*
[(Pisot)-243.6(g)0.3(raphs)-243.4(sho)28.3(wing)-244.5(t)0.3(hese)-243.1(n)27.9(um)28.3(b)-28.1(e)-0.1(rs)-243.4(to)-242.7(b)-28.1(e)-243.1(elemen)27.9(ts)-244.3(of)-243.8(the)]TJ
T*
-0.0002 Tc
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T*
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T*
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T*
[(construct)-304.1(graphs)-304.9(using)-304.1(a)-305(mixture)-304.6(of)-305.2(subgraphs)-304(from)-305(Fig-)]TJ
T*
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T*
-0.0002 Tc
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T*
[(from)-366.6(b)-28.2(e)-0.2(lo)28.2(w)-367.5(o)0.2(r)-366.5(f)0(rom)-366.6(a)0.2(b)-28.2(o)28.2(v)28(e)-0.2(,)-375.6(w)28.2(e)-367(c)-0.2(ould)-367(dene)-367(t)28.2(w)28.2(o)-367.4(t)28.2(y)0(p)-28.2(e)-0.2(s)-366.4(o)0.2(f)]TJ
T*
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[(10.)-1201.1(THE)-279(M)-0.2(AHLER)-280(MEASURE)-279.9(O)-0.2(F)-278.1(G)-0.1(RAPHS)]TJ
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ET
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BT
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[(\(1)-139.1(+)]TJ
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ET
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BT
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[(5\).)-431.6(Our)-291.5(denition)]TJ
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T*
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T*
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T*
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[(or)-337.9(at)-338.8(le)51.9(ast)]TJ
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19.9817 37.1685 TD
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[(W)82.7(e)-417.5(dene)-418.4(the)]TJ
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[(Mahler)-434.7(me)51.7(asur)51.3(e)]TJ
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[(\)o)418.8(fa)418.8(n)]TJ
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/F6 1 Tf
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9.9626 0 0 9.9626 522.3779 397.6501 Tm
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[(is)-316.6(the)-316.3(c)27.9(har-)]TJ
-19.7098 -1.3 TD
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[(acteristic)-274.9(p)-28.2(olynomial)-277.1(of)-274.6(its)-274.3(adjacency)-275.5(matrix,)-287(a)0.2(nd)]TJ
/F6 1 Tf
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[(of)-273.9(a)]TJ
-23.021 -1.3 TD
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[(p)-28.2(olynomial)-373.8(denotes)-371.8(its)-371.8(Mahler)-371.9(measure.)-558(Recall)-372(that)-372(for)]TJ
T*
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[(\))-355.7(its)-356.5(Mahler)-356.5(mea-)]TJ
-16.8859 -1.3 TD
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[(sure)-262.9(is)-264.1(dened)-263.8(to)-264.3(b)-28(e)]TJ
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[(ro)-27.8(cal)-369.2(p)-28.2(olynomial)]TJ
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9.9626 0 0 9.9626 475.911 319.944 Tm
(\()Tj
/F12 1 Tf
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()Tj
ET
488.088 327.32 m
493.164 327.32 l
S
BT
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9.9626 0 0 9.9626 488.088 319.944 Tm
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ET
524.079 327.32 m
529.155 327.32 l
S
BT
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9.9626 0 0 9.9626 524.079 319.944 Tm
(z)Tj
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[(\).)-552.8(This)-371.1(is)]TJ
-20.3892 -1.3 TD
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/F14 1 Tf
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9.9626 0 0 9.9626 523.116 306.993 Tm
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-18.5842 -1.3009 TD
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-1.1997 -1.3 TD
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[(cyclotomic)-336.3(graphs.)]TJ
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[(It)-519.1(turns)-518.1(o)0.3(ut)-520(that)-519.1(the)-519.6(c)-0.1(onnected)-519.6(graphs)-519(of)-519.3(smallest)]TJ
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[(Mahler)-264.3(measure)-263(b)-0.1(igger)-265.2(t)0.3(han)-263.9(1)-263.5(are)-263.9(all)-264.3(trees.)-420.6(U)0.1(sing)-264.4(the)-263.9(n)-0.1(o-)]TJ
T*
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[(tation)-371.6(of)-369.6([Cv)27.9(etk)27.9(o)28.1(vi)28.1()]TJ
8.2615 0 TD
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[(c)-373.2(a)0.3(nd)-369.6(Ro)28.3(wlinson)-371.4(90],)-379.1(dene)-368.7(the)-369.6(t)0.3(rees)]TJ
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[(a,)-165.9(b,)-165.9(c)]TJ
/F2 1 Tf
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[(\)a)336(n)335.6(d)]TJ
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[(a,)-165.9(b,)-165.9(c)]TJ
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[(\))-335.8(a)0.2(s)-333.9(i)0.2(n)-334.5(F)-0.6(igure)-333.6(15.)]TJ
/F3 1 Tf
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[(T)37.2(heor)11.1(em)-333.6(10.2.)]TJ
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(If)Tj
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-9.1965 -1.3 TD
[(me)51.7(asur)51.3(e)]TJ
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[(A)25.2(l)-51.5(l)-393(these)-393.6(gr)51.4(aphs)]TJ
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[(ar)51.4(e)-393.6(S)0.4(alem)-394.5(gr)51.4(aphs,)-402.4(e)0.3(xc)51.8(ept)]TJ
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[(whose)-547.2(p)51.4(olynomial)-550.2(has)-548.6(two)-547.6(z)-0.3(er)51.4(os)-548.6(on)]TJ
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[(,)-599.2(s)-0.2(o)-548.4(that)-547.5(al)-51.4(l)]TJ
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[(ap)51.4(art)-588.2(fr)51.4(om)]TJ
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[(ar)51.3(e)-587.9(S)0.3(alem)-588.8(numb)51.7(ers.)]TJ
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()Tj
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[(and)-326.2(the)-325.8(gr)51.4(aph)]TJ
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(k)Tj
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[(,)-357.3(w)-0.5(hich)-357.9(appr)51.3(o)51.3(a)-0.2(ch)]TJ
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[(F)76.5(u)0.2(rthermor)51.4(e,)-426.8(the)-412.6(only)]TJ
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(7)Tj
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(10)Tj
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[(,)-349.2(these)-338.6(values)-339.1(incr)51.3(e)51.7(a)-0.2(sing)-341.3(with)]TJ
/F6 1 Tf
12.9889 0 TD
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/F11 1 Tf
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0.454 Tc
[(.\()453.6(A)479.1(l)453.9(s)453.6(o)]TJ
/F6 1 Tf
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0 Tc
(M)Tj
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(T)Tj
/F2 1 Tf
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(,)Tj
/F2 1 Tf
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[(9\)\))-281.8(=)]TJ
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(M)Tj
/F2 1 Tf
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(\()Tj
/F6 1 Tf
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(T)Tj
/F2 1 Tf
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/F6 1 Tf
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(,)Tj
/F2 1 Tf
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(3)Tj
/F6 1 Tf
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(,)Tj
/F2 1 Tf
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(4\)\))Tj
/F11 1 Tf
1.2765 0 TD
(.\))Tj
/F2 1 Tf
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[(In)-313.6([Hironak)55.2(a)-315(01,)-318.6(Theorem)-314.1(1.1],)-319.5(Hironak)55.2(a)-315(sho)28.3(w)0.3(s)-313.9(e)-0.1(ssen-)]TJ
-1.1997 -1.3 TD
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[(tially)-466.1(that)-464.1(Lehmers)-464(n)27.8(u)-0.2(m)28.2(b)-28.2(er)]TJ
/F6 1 Tf
13.212 0 TD
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()Tj
/F13 1 Tf
6.9738 0 0 6.9738 176.886 397.38 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 186.291 398.874 Tm
(=)Tj
/F6 1 Tf
1.272 0 TD
(M)Tj
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/F6 1 Tf
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(T)Tj
/F2 1 Tf
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/F6 1 Tf
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/F2 1 Tf
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(2)Tj
/F6 1 Tf
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(,)Tj
/F2 1 Tf
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[(6\)\))-467.8(is)-464.1(the)]TJ
-20.3314 -1.3 TD
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[(smallest)-401.7(Mahler)-401.6(measure)-401.2(o)0.3(f)-401.9(a)-400.8(star-lik)28.1(e)-402.1(t)0.3(ree.)-647.4(The)-401.2(g)0.3(raph)]TJ
T*
[(Pisot)-249(n)27.9(um)28.3(b)-28.1(e)-0.1(rs)-248(in)-248.6(Theorem)-248.1(10.2)-249(ha)28.3(v)28.1(e)-249.5(b)-28.1(een)-247.7(sho)28.3(w)0.3(n)-248.6(b)27.9(y)-248.3(H)0.1(o-)]TJ
T*
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[(man)-247.9([Homan)-248.8(72])-247.4(to)-247.4(b)-28.3(e)-246.9(limit)-248.3(p)-28.3(oin)27.7(ts)-248.2(of)-247.6(transformed)-247.9(g)0.1(raph)]TJ
T*
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[(indices,)-284.3(w)0.2(hic)27.8(h)-273(is)-272.5(equiv)55.1(alen)27.8(t)-273.5(to)-272.6(our)-272.5(r)-0.6(epresen)27.8(tation)-273(of)-271.9(them)]TJ
T*
[(as)-333.9(limits)-335.7(of)-334.2(graph)-333.6(S)-0.2(alem)-334.9(n)27.8(um)28.2(b)-28.2(e)-0.2(rs.)]TJ
1.1997 -1.3 TD
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[(It)-565.2(is)-565(clear)-566(h)-0.1(o)28.3(w)-565.2(to)-566.1(extend)-564.7(the)-565.6(t)0.3(heorem)-565.2(t)0.3(o)-565.2(n)-0.1(oncon-)]TJ
-1.1997 -1.3009 TD
[(nected)-343.4(graphs:)-462.2(s)-0.4(ince)]TJ
/F6 1 Tf
9.2732 0 TD
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 138.771 311.826 Tm
(3)Tj
-0.1613 -0.8724 TD
(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 146.16 308.208 Tm
0.2927 Tc
(>)Tj
/F2 1 Tf
1.5872 0 TD
0.3443 Tc
[(,f)344.5(o)344.7(r)1.5(s)344(u)344.3(c)372.3(h)1.9(ag)344.7(r)343.9(a)344.7(p)344.3(h)]TJ
/F6 1 Tf
8.1151 0 TD
0 Tc
(G)Tj
/F2 1 Tf
1.1292 0 TD
-0.0002 Tc
[(to)-343.1(ha)28.2(v)28(e)]TJ
/F6 1 Tf
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0 Tc
(M)Tj
/F2 1 Tf
1.0795 0 TD
(\()Tj
/F6 1 Tf
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(G)Tj
/F2 1 Tf
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(\))Tj
/F12 1 Tf
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()Tj
/F2 1 Tf
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/F6 1 Tf
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-5.9298 -1.3 TD
[(b)-28.2(e)-323.6(as)-323.9(describ)-28.2(ed)-323.6(in)-323.6(the)-324.5(t)0.2(heorem,)-326.8(with)-324.5(all)-325(other)-324(connected)]TJ
T*
[(comp)-28.2(onen)27.8(ts)-458.5(cyclotomic.)-818.2(U)0(sing)-457.8(the)-457.3(r)-0.6(esults)-457.6(of)-457.1(Theorem)]TJ
T*
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[(10.2,)-334.8(it)-333.9(is)-334.7(an)-333.5(easy)-333.2(exercise)-333.5(to)-333.9(c)27.9(hec)27.9(k)-334.1(t)0.3(he)-333.5(p)-28.1(o)0.3(ssibilities.)]TJ
/F11 1 Tf
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[(P)-51.4(roo)-51.5(f)-50.9(:)]TJ
/F2 1 Tf
3.132 0 TD
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[(The)-355.1(p)-0.1(ro)-27.7(of)-354.9(dep)-28.1(ends)-354.6(hea)28.3(vily)-355.8(on)-355.2(results)-354.6(of)-355.8(Brou)27.9(w)28.3(e)-0.1(r)]TJ
-3.132 -1.3 TD
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[(and)-229.7(N)0(eumaier)-231([)0.2(Brou)27.8(w)28.2(e)-0.2(r)-230.1(a)0.2(nd)-229.7(Neumaier)-231(89])-230.1(and)-228.8(C)0.2(v)28(e)-0.2(tk)28(o)28.2(v)0(i)28.2()]TJ
23.8738 0 TD
0 Tc
(c,)Tj
-23.8738 -1.3009 TD
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[(Do)-27.8(ob,)-450.5(a)0.2(nd)-427.5(Gutman)-428.4([Cv)28(etk)28(o)28.2(vi)28.2()]TJ
13.2653 0 TD
[(c)-431.1(e)-0.2(t)-427.1(al.)-726.1(82],)-451.4(as)-427.8(describ)-28.2(ed)]TJ
-13.2653 -1.3 TD
[(con)27.8(v)28(enien)27.8(tly)-457.1(b)27.8(y)-454.4(Cv)28(etk)28(o)28.2(vi)28.2()]TJ
11.2101 0 TD
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[(c)-459(a)0.3(nd)-454.5(Ro)28.3(wlinson)-456.3(i)0.3(n)-455.4(t)0.3(heir)-454.9(s)-0.4(ur-)]TJ
-11.2101 -1.3 TD
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[(v)27.9(e)-0.3(y)-424.7(p)-0.3(ap)-28.3(er)-424.4([Cv)27.9(etk)27.9(o)28.1(vi)28.1()]TJ
8.902 0 TD
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[(c)-429.3(a)0.2(nd)-424.8(Ro)28.2(wlinson)-425.7(90,)-447.8(Theorem)-425.3(2.4].)]TJ
-8.902 -1.3 TD
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[(These)-516.9(r)-0.5(esults)-516.3(tell)-517.3(us)-516.3(precisely)-516.6(whc)27.9(h)-516.9(connected)-516.9(graphs)]TJ
T*
[(ha)28.3(v)28.1(e)-450.9(largest)-451.4(eigen)27.9(v)55.2(alue)-451.8(i)0.3(n)-450(t)0.3(he)-450.9(in)27.9(terv)55.2(al)-450.4(\(2)]TJ
/F6 1 Tf
18.4047 0 TD
0 Tc
(,)Tj
/F23 1 Tf
0.4433 0.9928 TD
()Tj
ET
0 0 0 1 K
0 J 0 j 0.405 w 10 M []0 d
1 i
238.662 166.958 m
269.109 166.958 l
S
BT
/F2 1 Tf
9.9626 0 0 9.9626 238.662 156.864 Tm
0.2227 Tc
(2+)Tj
/F12 1 Tf
1.7227 0.8275 TD
0 Tc
()Tj
ET
264.123 165.311 m
269.109 165.311 l
S
BT
/F2 1 Tf
9.9626 0 0 9.9626 264.1231 156.8641 Tm
0.1667 Tc
[(5])-305.3(=)]TJ
-22.4055 -1.3 TD
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(\(2)Tj
/F6 1 Tf
0.888 0 TD
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(,)Tj
/F2 1 Tf
0.4436 0 TD
(2)Tj
/F6 1 Tf
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(.)Tj
/F2 1 Tf
0.2773 0 TD
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(058)Tj
/F6 1 Tf
1.6649 0 TD
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(...)Tj
/F2 1 Tf
1.1708 0 TD
-0.0002 Tc
[(].)-928.4(They)-495.1(are)-495.3(all)-495.7(trees)-494.7(of)-495(the)-494.4(f)0(orm)]TJ
/F6 1 Tf
15.8752 0 TD
0 Tc
(T)Tj
/F2 1 Tf
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BT
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313.431 683.634 l
S
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307.743 683.634 l
B*
334.743 713.334 m
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B*
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318.291 713.334 m
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312.891 713.334 m
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S
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296.955 685.13 298.165 686.34 299.655 686.34 c
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b*
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361.743 683.634 l
B*
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B*
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b*
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340.155 655.43 341.365 656.64 342.855 656.64 c
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361.743 683.634 l
B*
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359.055 685.13 360.265 686.34 361.755 686.34 c
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b*
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341.365 680.94 340.155 682.15 340.155 683.64 c
340.155 685.13 341.365 686.34 342.855 686.34 c
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b*
0.54 w
342.843 683.634 m
361.743 683.634 l
B*
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359.055 685.13 360.265 686.34 361.755 686.34 c
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b*
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340.155 685.13 341.365 686.34 342.855 686.34 c
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b*
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280.743 653.934 m
299.643 653.934 l
B*
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302.355 653.94 m
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298.165 651.24 296.955 652.45 296.955 653.94 c
296.955 655.43 298.165 656.64 299.655 656.64 c
301.145 656.64 302.355 655.43 302.355 653.94 c
b*
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283.455 652.45 282.245 651.24 280.755 651.24 c
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278.055 655.43 279.265 656.64 280.755 656.64 c
282.245 656.64 283.455 655.43 283.455 653.94 c
b*
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280.743 683.634 m
299.643 683.634 l
B*
440.043 583.734 m
445.443 583.734 l
B*
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288.855 583.74 m
288.855 582.25 287.645 581.04 286.155 581.04 c
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283.455 585.23 284.665 586.44 286.155 586.44 c
287.645 586.44 288.855 585.23 288.855 583.74 c
b*
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269.955 582.25 268.745 581.04 267.255 581.04 c
265.765 581.04 264.555 582.25 264.555 583.74 c
264.555 585.23 265.765 586.44 267.255 586.44 c
268.745 586.44 269.955 585.23 269.955 583.74 c
b*
269.955 583.74 m
269.955 582.25 268.745 581.04 267.255 581.04 c
265.765 581.04 264.555 582.25 264.555 583.74 c
264.555 585.23 265.765 586.44 267.255 586.44 c
268.745 586.44 269.955 585.23 269.955 583.74 c
b*
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251.055 582.25 249.845 581.04 248.355 581.04 c
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245.655 585.23 246.865 586.44 248.355 586.44 c
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b*
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340.143 583.734 m
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B*
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335.031 583.734 l
329.091 583.734 m
329.631 583.734 l
323.691 583.734 m
324.231 583.734 l
318.291 583.734 m
318.831 583.734 l
S
307.743 583.734 m
313.143 583.734 l
B*
386.043 583.734 m
404.943 583.734 l
B*
367.143 602.634 m
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B*
367.143 583.734 m
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B*
348.243 583.734 m
367.143 583.734 l
B*
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407.655 583.74 m
407.655 582.25 406.445 581.04 404.955 581.04 c
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402.255 585.23 403.465 586.44 404.955 586.44 c
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b*
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388.755 582.25 387.545 581.04 386.055 581.04 c
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383.355 585.23 384.565 586.44 386.055 586.44 c
387.545 586.44 388.755 585.23 388.755 583.74 c
b*
367.155 581.04 m
365.665 581.04 364.455 582.25 364.455 583.74 c
364.455 585.23 365.665 586.44 367.155 586.44 c
368.645 586.44 369.855 585.23 369.855 583.74 c
369.855 582.25 368.645 581.04 367.155 581.04 c
b*
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368.645 605.34 369.855 604.13 369.855 602.64 c
369.855 601.15 368.645 599.94 367.155 599.94 c
b*
388.755 583.74 m
388.755 582.25 387.545 581.04 386.055 581.04 c
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383.355 585.23 384.565 586.44 386.055 586.44 c
387.545 586.44 388.755 585.23 388.755 583.74 c
b*
369.855 583.74 m
369.855 582.25 368.645 581.04 367.155 581.04 c
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364.455 585.23 365.665 586.44 367.155 586.44 c
368.645 586.44 369.855 585.23 369.855 583.74 c
b*
369.855 583.74 m
369.855 582.25 368.645 581.04 367.155 581.04 c
365.665 581.04 364.455 582.25 364.455 583.74 c
364.455 585.23 365.665 586.44 367.155 586.44 c
368.645 586.44 369.855 585.23 369.855 583.74 c
b*
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350.955 582.25 349.745 581.04 348.255 581.04 c
346.765 581.04 345.555 582.25 345.555 583.74 c
345.555 585.23 346.765 586.44 348.255 586.44 c
349.745 586.44 350.955 585.23 350.955 583.74 c
b*
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265.765 599.94 264.555 601.15 264.555 602.64 c
264.555 604.13 265.765 605.34 267.255 605.34 c
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269.955 601.15 268.745 599.94 267.255 599.94 c
b*
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428.991 583.734 m
429.531 583.734 l
423.591 583.734 m
424.131 583.734 l
418.191 583.734 m
418.731 583.734 l
S
407.643 583.734 m
413.043 583.734 l
B*
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450.855 583.74 m
450.855 582.25 449.645 581.04 448.155 581.04 c
446.665 581.04 445.455 582.25 445.455 583.74 c
445.455 585.23 446.665 586.44 448.155 586.44 c
449.645 586.44 450.855 585.23 450.855 583.74 c
b*
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205.143 583.734 l
B*
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202.455 585.23 203.665 586.44 205.155 586.44 c
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b*
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188.955 582.25 187.745 581.04 186.255 581.04 c
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183.555 585.23 184.765 586.44 186.255 586.44 c
187.745 586.44 188.955 585.23 188.955 583.74 c
b*
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240.243 583.734 m
245.643 583.734 l
B*
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229.731 583.734 l
223.791 583.734 m
224.331 583.734 l
218.391 583.734 m
218.931 583.734 l
S
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B*
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B*
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B*
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B*
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B*
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302.355 585.23 303.565 586.44 305.055 586.44 c
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b*
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288.855 582.25 287.645 581.04 286.155 581.04 c
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283.455 585.23 284.665 586.44 286.155 586.44 c
287.645 586.44 288.855 585.23 288.855 583.74 c
b*
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268.745 586.44 269.955 585.23 269.955 583.74 c
269.955 582.25 268.745 581.04 267.255 581.04 c
b*
EMC
BT
/F14 1 Tf
6.9738 0 0 6.9738 305.8677 728.4451 Tm
0 0 0 1 k
0 Tc
(a)Tj
/F23 1 Tf
9.9626 0 0 9.9626 280.9827 722.2621 Tm
(\012)Tj
ET
0 0 0 1 K
1.197 w
285.465 722.861 m
303.546 722.861 l
S
BT
9.9626 0 0 9.9626 303.5458 722.2621 Tm
-0.0001 Tc
()Tj
ET
312.51 722.861 m
330.591 722.861 l
S
BT
9.9626 0 0 9.9626 330.5909 722.2621 Tm
0 Tc
(\015)Tj
/F14 1 Tf
6.9738 0 0 6.9738 306.0524 697.827 Tm
(b)Tj
/F23 1 Tf
9.9626 0 0 9.9626 280.7625 691.644 Tm
(\012)Tj
ET
285.244 692.243 m
303.325 692.243 l
S
BT
9.9626 0 0 9.9626 303.3255 691.644 Tm
-0.0001 Tc
()Tj
ET
312.289 692.243 m
330.37 692.243 l
S
BT
9.9626 0 0 9.9626 330.3706 691.644 Tm
0 Tc
(\015)Tj
/F14 1 Tf
6.9738 0 0 6.9738 306.168 669.045 Tm
(c)Tj
/F23 1 Tf
9.9626 0 0 9.9626 280.905 662.8711 Tm
(\012)Tj
ET
285.387 663.47 m
303.468 663.47 l
S
BT
9.9626 0 0 9.9626 303.468 662.8711 Tm
-0.0001 Tc
()Tj
ET
312.432 663.47 m
330.513 663.47 l
S
BT
9.9626 0 0 9.9626 330.5132 662.8711 Tm
0 Tc
(\015)Tj
/F6 1 Tf
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(T)Tj
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(\()Tj
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[(a,)-165.9(b,)-165.9(c)]TJ
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(\))Tj
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[(a,)-165.9(b,)-165.9(c)]TJ
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(\))Tj
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()Tj
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(\012)Tj
ET
190.965 592.523 m
209.046 592.523 l
S
BT
9.9626 0 0 9.9626 209.0458 591.9241 Tm
-0.0001 Tc
()Tj
ET
218.01 592.523 m
236.091 592.523 l
S
BT
9.9626 0 0 9.9626 236.0909 591.9241 Tm
0 Tc
(\015)Tj
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()Tj
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(\012)Tj
ET
290.644 592.343 m
308.725 592.343 l
S
BT
9.9626 0 0 9.9626 308.7255 591.744 Tm
-0.0001 Tc
()Tj
ET
317.689 592.343 m
335.77 592.343 l
S
BT
9.9626 0 0 9.9626 335.7706 591.744 Tm
0 Tc
(\015)Tj
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(c)Tj
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(\012)Tj
ET
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S
BT
9.9626 0 0 9.9626 408.768 591.9241 Tm
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()Tj
ET
417.732 592.523 m
435.813 592.523 l
S
BT
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[(.)-456.4(T)-0.6(he)-341.9(trees)]TJ
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[(a,)-172.4(b,)-171.4(c)]TJ
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[(,b)165.9(,)]TJ
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(2)Tj
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()Tj
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(11\)\))Tj
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[(20.)-532.8(Cases)]TJ
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(b)Tj
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[(=1)327.5(4)]TJ
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(,...,)Tj
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[(19)-364.5(m)28.4(u)0(st)-361.8(b)-28(e)-362.3(c)28(hec)28(k)28.2(e)0(d)]TJ
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()Tj
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(Q)Tj
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[(,b)165.9(,)]TJ
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(4\)\))Tj
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(2)Tj
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(6\)\))Tj
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(3)Tj
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(,b)Tj
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()Tj
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(8\)\))Tj
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(>)Tj
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()Tj
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[(14.)-446(Chec)27.8(k)]TJ
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(b)Tj
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[(=1)278.7(1)]TJ
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(12)Tj
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(,)Tj
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[(13)-336.8(individually;)]TJ
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[(,b)165.9(,)]TJ
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[(12.)-446(Chec)27.8(k)]TJ
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[(=1)278.7(0)]TJ
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[(,b)165.9(,)]TJ
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[(Chec)27.9(k)]TJ
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[(=1)278.7(0)]TJ
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[(,b)165.9(,)]TJ
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[(11.)-446(Chec)27.8(k)]TJ
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[(,b)165.9(,)]TJ
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[(Chec)27.9(k)]TJ
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[(=)-278.7(10;)]TJ
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[(Fo)-82.3(r)]TJ
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[(,b)165.9(,c)]TJ
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[(,b)165.9(,)]TJ
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[(10.)-446(Chec)27.8(k)]TJ
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[(=9)278.7(;)]TJ
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[(,b)165.9(,)]TJ
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(,b)Tj
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(6\)\))Tj
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()Tj
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-0.0002 Tc
[(9.)-445.1(Chec)27.8(k)]TJ
/F6 1 Tf
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(b)Tj
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[(=8)277.8(;)]TJ
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()Tj
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[(Fo)-82.3(r)]TJ
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(\()Tj
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(Q)Tj
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(\(4)Tj
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[(,b)165.9(,c)]TJ
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(,)Tj
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/F6 1 Tf
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[(Fo)-82.3(r)]TJ
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(Q)Tj
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[(a,)-165.9(b,)-165.9(c)]TJ
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(4)Tj
/F6 1 Tf
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(,b)Tj
/F12 1 Tf
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(5\)\))Tj
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/F18 1 Tf
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()Tj
/F2 1 Tf
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(8.)Tj
18.8452 43.054 TD
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[(W)82.6(e)-384.2(remark)-384.8(t)0.2(hat)-386.4(i)0.2(t)-384.6(i)0.2(s)-385.4(s)-0.5(traigh)27.8(tforw)28.2(a)0.2(rd,)-400.9(with)-386(computer)]TJ
-1.1997 -1.3 TD
[(assistance,)-599.6(using)-546.3(L)-0.3(emma)-546.3(7.1,)-600.5(to)-546.3(mak)28(e)-546.8(t)0.2(he)-546.8(c)27.8(hec)27.8(ks)-546.2(re-)]TJ
T*
-0.0001 Tc
[(quired)-358.8(in)-358.8(the)-358.8(p)-0.1(ro)-27.7(of.)-520.9(D)-0.5(enoting)-359.2(b)27.9(y)]TJ
/F6 1 Tf
14.8878 0 TD
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(q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 478.782 480.6931 Tm
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 483.678 482.187 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
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[(a,)-165.9(b,)-165.9(c)]TJ
/F2 1 Tf
2.2774 0 TD
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[(\))-361.1(t)0.2(he)-359.8(quotien)27.8(t)]TJ
-18.4912 -1.3 TD
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(of)Tj
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(Q)Tj
/F2 1 Tf
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(\()Tj
/F6 1 Tf
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[(a,)-165.9(b,)-165.9(c)]TJ
/F2 1 Tf
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[(\))-458.7(with)-456.4(ro)-27.8(ot)-456(at)-456(the)]TJ
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(k)Tj
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[(th)-456.4(v)28(e)-0.2(rtex)-456.2(of)-455.3(the)-456.4(cen)27.8(tral)]TJ
-13.9672 -1.3 TD
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[(path,)-500.1(a)0.3(nd)-466.3(b)27.9(y)]TJ
/F6 1 Tf
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(t)Tj
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[(a,)-165.9(b,)-165.9(c)]TJ
/F2 1 Tf
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[(\))-468.6(t)0.2(he)-466.4(quotien)27.8(t)-468.6(of)]TJ
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(T)Tj
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(\()Tj
/F6 1 Tf
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[(a,)-165.9(b,)-165.9(c)]TJ
/F2 1 Tf
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0.4684 Tc
[(\)h)468.4(a)496.8(v)468.6(i)468.8(n)468.4(g)]TJ
-20.8537 -1.3 TD
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[(ro)-27.7(ot)-377.3(at)-378.2(the)-377.7(endv)28.1(ertex)-377.5(o)0.3(f)-378.4(t)0.3(he)]TJ
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(c)Tj
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[(-path,)-389.1(t)0.2(his)-378.1(l)0.2(emma)-379.2(tells)-378.1(us)]TJ
-13.2301 -1.3 TD
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(that)Tj
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3.2946 -2.5466 TD
0 Tc
(q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 363.285 403.518 Tm
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 368.181 405.012 Tm
(\()Tj
/F6 1 Tf
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[(a,)-165.9(b,)-165.9(c)]TJ
/F2 1 Tf
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[(\)=)280.5(\()]TJ
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(z)Tj
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(+1)Tj
/F12 1 Tf
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(t)Tj
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(1)Tj
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(1)Tj
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(,b)Tj
/F12 1 Tf
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(1)Tj
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(k)Tj
/F2 1 Tf
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(\)\)\))Tj
/F15 1 Tf
6.9738 0 0 6.9738 524.799 393.186 Tm
0 Tc
()Tj
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(1)Tj
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9.9626 0 0 9.9626 535.509 389.073 Tm
(,)Tj
-17.156 -1.5999 TD
(t)Tj
/F2 1 Tf
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(\()Tj
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[(a,)-165.9(b,)-165.9(c)]TJ
/F2 1 Tf
2.2774 0 TD
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[(\)=)279.6(\()]TJ
/F6 1 Tf
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(z)Tj
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(+1)Tj
/F12 1 Tf
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(zt)Tj
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(\()Tj
/F6 1 Tf
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[(a,)-165.9(b,)-165.9(c)]TJ
/F12 1 Tf
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(1\)\))Tj
/F15 1 Tf
6.9738 0 0 6.9738 507.582 377.247 Tm
0 Tc
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(1)Tj
/F6 1 Tf
9.9626 0 0 9.9626 518.292 373.134 Tm
(,)Tj
/F2 1 Tf
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(t)Tj
/F2 1 Tf
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(\()Tj
/F6 1 Tf
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[(a,)-165.9(b,)]TJ
/F2 1 Tf
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[(0\))-635(=)]TJ
/F13 1 Tf
6.9738 0 0 6.9738 407.097 349.6711 Tm
0 Tc
(\()Tj
/F14 1 Tf
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(z)Tj
/F21 1 Tf
4.9813 0 0 4.9813 414.306 352.677 Tm
(a)Tj
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/F15 1 Tf
6.9738 0 0 6.9738 427.167 349.6711 Tm
0 Tc
()Tj
/F13 1 Tf
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(1\)\()Tj
/F14 1 Tf
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(z)Tj
/F21 1 Tf
4.9813 0 0 4.9813 447.687 352.677 Tm
(b)Tj
/F22 1 Tf
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(+1)Tj
/F15 1 Tf
6.9738 0 0 6.9738 459.846 349.6711 Tm
0 Tc
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
ET
0.405 w
407.097 347.336 m
473.166 347.336 l
S
BT
6.9738 0 0 6.9738 409.041 341.283 Tm
0 Tc
(\()Tj
/F14 1 Tf
0.4465 0 TD
(z)Tj
/F15 1 Tf
0.5872 0 TD
()Tj
/F13 1 Tf
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(1\)\()Tj
/F14 1 Tf
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(z)Tj
/F21 1 Tf
4.9813 0 0 4.9813 436.77 343.272 Tm
(a)Tj
/F22 1 Tf
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(b)Tj
/F22 1 Tf
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(+2)Tj
/F15 1 Tf
6.9738 0 0 6.9738 457.902 341.283 Tm
0 Tc
()Tj
/F13 1 Tf
0.8931 0 TD
-0.0003 Tc
(1\))Tj
/F2 1 Tf
9.9626 0 0 9.9626 474.354 344.838 Tm
-0.0002 Tc
[(,)-599.6(t)0.2(he)-546.8(quotien)27.8(t)-548.1(of)-547.4(the)]TJ
-14.8894 -1.3 TD
[(ro)-27.8(oted)-321.8(p)-0.2(ath)]TJ
/F6 1 Tf
5.4501 0 TD
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(A)Tj
/F14 1 Tf
6.9738 0 0 6.9738 387.783 330.393 Tm
(a)Tj
/F13 1 Tf
0.6195 0 TD
(+)Tj
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(b)Tj
/F13 1 Tf
0.502 0 TD
0.0006 Tc
(+1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 412.317 331.887 Tm
0 Tc
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/F6 1 Tf
0.3885 0 TD
(a)Tj
/F2 1 Tf
0.7263 0 TD
0.1979 Tc
(+1)Tj
/F6 1 Tf
1.4752 0 TD
0.1658 Tc
(,b)Tj
/F2 1 Tf
1.0723 0 TD
0.1979 Tc
[(+1)198.3(\))]TJ
/F6 1 Tf
1.8637 0 TD
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(.)Tj
/F2 1 Tf
0.5998 0 TD
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[(Then)-321.8(the)-321.8(denominator)]TJ
-14.7883 -1.3 TD
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1.1301 0 TD
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(q)Tj
/F14 1 Tf
6.9738 0 0 6.9738 341.721 317.442 Tm
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 346.626 318.936 Tm
(\()Tj
/F6 1 Tf
0.3885 0 TD
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[(a,)-165.9(b,)-165.9(c)]TJ
/F2 1 Tf
2.2774 0 TD
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[(\))-326.8(giv)28(es)-326.7(the)-325.4(r)-0.6(ecipro)-27.8(c)-0.2(al)-325(p)-28.2(olynomial)-327.7(of)]TJ
/F6 1 Tf
15.7397 0 TD
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(Q)Tj
/F2 1 Tf
0.7905 0 TD
(\()Tj
/F6 1 Tf
0.3885 0 TD
-0.0001 Tc
[(a,)-165.9(b,)-165.9(c)]TJ
/F2 1 Tf
2.2774 0 TD
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(\),)Tj
-23.9307 -1.3 TD
-0.0002 Tc
[(at)-422.5(least)-422.5(u)-0.2(p)-422.1(t)0.2(o)-422.6(a)-422.6(c)-0.2(yclotomic)-424.8(factor)-423.4(\(one)-423(c)-0.2(an)-423(sho)28.2(w)-421.7(using)]TJ
T*
-0.0003 Tc
[(Lemma)-463.3(2.3\(i\))-464.2(and)-462.9(L)-0.4(emma)-463.3(7.1\(i\))-464.2(that)-463.3(all)-463.3(ro)-27.9(ots)-463.2(greater)]TJ
T*
-0.0002 Tc
[(than)-407.6(1)-407.2(o)0.2(f)-407.4(t)0.2(he)-406.7(recipro)-27.8(c)-0.2(al)-407.2(p)-28.2(olynomial)-409.9(of)]TJ
/F6 1 Tf
17.4362 0 TD
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(Q)Tj
/F2 1 Tf
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(\()Tj
/F6 1 Tf
0.3885 0 TD
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[(a,)-165.9(b,)-165.9(c)]TJ
/F2 1 Tf
2.2774 0 TD
0.4088 Tc
[(\)a)409.2(r)408.4(e)1.4(i)409.2(n)408.8(-)]TJ
-20.8926 -1.3 TD
-0.0002 Tc
[(deed)-333.6(p)-28.2(oles)-333.9(o)0.2(f)-334.2(its)-333.9(quotien)27.8(t\).)]TJ
1.1997 -1.3 TD
-0.0003 Tc
[(Concerning)-338.6(the)-338.2(limit)-340.4(p)-28.3(oin)27.7(ts)-338.5(of)]TJ
/F6 1 Tf
13.558 0 TD
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(M)Tj
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(\()Tj
/F6 1 Tf
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(G)Tj
/F2 1 Tf
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(\))Tj
/F12 1 Tf
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( )Tj
/F2 1 Tf
0.8916 0 TD
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([1)Tj
/F6 1 Tf
0.7769 0 TD
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(,)Tj
/F2 1 Tf
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[(\),)-341.3(one)-339.1(c)-0.3(an)]TJ
-20.2548 -1.3 TD
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[(c)27.9(hec)27.9(k)-333.2(t)0.3(hat)]TJ
/F12 1 Tf
1 -2.3461 TD
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()Tj
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(M)Tj
/F2 1 Tf
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(T)Tj
/F2 1 Tf
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(\(1)Tj
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[(,b)165.9(,c)]TJ
/F2 1 Tf
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(\)\))Tj
/F12 1 Tf
1.0579 0 TD
0 Tc
()Tj
/F6 1 Tf
1.2774 0 TD
(M)Tj
/F2 1 Tf
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(\()Tj
/F6 1 Tf
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[(in)-389.6(lo)28.2(w)28.2(e)-0.2(st)-390(terms,)-403.6(then)-388.7(from)-389.1(Lemma)-390(7.1\(ii\))]TJ
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(R)Tj
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(T)Tj
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4.9813 0 0 4.9813 227.709 379.236 Tm
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9.9626 0 0 9.9626 235.413 381.729 Tm
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(.)Tj
/F2 1 Tf
-16.8633 -2.0199 TD
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[(No)28.2(w)]TJ
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(z)Tj
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6.9738 0 0 6.9738 89.307 325.452 Tm
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/F2 1 Tf
9.9626 0 0 9.9626 93.771 321.3391 Tm
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(\)=\()Tj
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/F2 1 Tf
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(z)Tj
/F13 1 Tf
6.9738 0 0 6.9738 168.111 325.452 Tm
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9.9626 0 0 9.9626 172.575 321.3391 Tm
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(\()Tj
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/F2 1 Tf
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(\)+)Tj
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(z)Tj
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(\)\))Tj
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(,)Tj
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/F2 1 Tf
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[(.)-414.3(H)0.1(ence,)-263.4(if)]TJ
/F6 1 Tf
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()Tj
/F12 1 Tf
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()Tj
/F2 1 Tf
T*
0.2783 Tc
(=0)Tj
-23.0445 -1.3 TD
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(and)Tj
/F6 1 Tf
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(f)Tj
/F2 1 Tf
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(\()Tj
/F6 1 Tf
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()Tj
/F2 1 Tf
0.5502 0 TD
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[(\))-302.4(=)-302.9(0,)-352.1(then)]TJ
/F12 1 Tf
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0 Tc
()Tj
ET
135.765 295.64 m
141.255 295.64 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 135.7651 288.264 Tm
()Tj
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0.8989 0 TD
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(and)Tj
/F12 1 Tf
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()Tj
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()Tj
ET
180.288 295.64 m
185.778 295.64 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 180.288 288.264 Tm
()Tj
/F2 1 Tf
0.898 0 TD
-0.0002 Tc
[(are)-348(r)-0.6(o)-27.8(ots)-349.2(of)-348.7(the)-348.9(d)-0.2(ier-)]TJ
-14.8885 -1.3 TD
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[(en)27.9(t)-333(f)0.1(actors)-334.7(o)0.3(f)]TJ
/F6 1 Tf
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/F2 1 Tf
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(\()Tj
/F6 1 Tf
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(z)Tj
/F13 1 Tf
6.9738 0 0 6.9738 116.478 278.922 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 120.951 275.313 Tm
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[(\))-333(a)0.3(nd)-333.5(are)-333.5(n)-0.1(ot)-333.9(algebraic)-334.4(conjugates.)-446.8(In)]TJ
-8.0346 -1.3 TD
[(particular,)-473.9(i)0.3(f)]TJ
/F6 1 Tf
6.0617 0 TD
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()Tj
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/F12 1 Tf
13.715 0.72 TD
0 Tc
()Tj
ET
256.149 269.738 m
261.639 269.738 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 256.149 262.3621 Tm
()Tj
/F2 1 Tf
0.5502 0 TD
0.7783 Tc
[(.W)861.1(e)]TJ
-22.1553 -1.3 TD
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[(can)-304.6(a)0.3(pply)-305.2(t)0.3(his)-304.9(c)-0.1(onstruction)-305.5(regardless)-304(o)0.3(f)-304.3(t)0.3(he)-304.6(v)55.2(alue)-305.5(o)0.3(f)-304.3(t)0.3(he)]TJ
T*
-0.0003 Tc
[(quotien)27.7(t)-374.8(of)]TJ
/F6 1 Tf
5.1628 0 TD
0 Tc
(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 98.163 234.966 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 102.627 236.46 Tm
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/F6 1 Tf
13.8091 0 TD
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()Tj
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(2)Tj
-0.1613 -0.8724 TD
(2)Tj
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9.9626 0 0 9.9626 250.155 236.46 Tm
(,)Tj
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0.6604 0 TD
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 262.215 240.069 Tm
(2)Tj
-0.1613 -0.8724 TD
(3)Tj
/F2 1 Tf
9.9626 0 0 9.9626 266.688 236.46 Tm
(,)Tj
/F6 1 Tf
0.6604 0 TD
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 278.748 240.069 Tm
(2)Tj
-0.1613 -0.8724 TD
(5)Tj
/F2 1 Tf
9.9626 0 0 9.9626 283.221 236.46 Tm
(,)Tj
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-24.3225 -1.3 TD
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 46.386 227.1181 Tm
(2)Tj
-0.1613 -0.8724 TD
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(12)Tj
/F2 1 Tf
9.9626 0 0 9.9626 53.703 223.509 Tm
0 Tc
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0.6107 0 TD
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 65.268 227.1181 Tm
(2)Tj
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(21)Tj
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9.9626 0 0 9.9626 72.585 223.509 Tm
0 Tc
(,)Tj
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0.6116 0 TD
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 84.159 227.1181 Tm
(2)Tj
-0.1613 -0.8724 TD
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(23)Tj
/F2 1 Tf
9.9626 0 0 9.9626 91.467 223.509 Tm
0.3338 Tc
[(,a)334.2(n)333.8(d)]TJ
/F6 1 Tf
2.5557 0 TD
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()Tj
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6.9738 0 0 6.9738 122.409 227.1181 Tm
(2)Tj
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(41)Tj
/F2 1 Tf
9.9626 0 0 9.9626 133.047 223.509 Tm
[(as)-334(elemen)27.7(ts)-334.9(of)]TJ
/F6 1 Tf
6.4556 0 TD
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(T)Tj
/F13 1 Tf
6.9738 0 0 6.9738 203.184 222.0151 Tm
-0.0001 Tc
(graph)Tj
/F2 1 Tf
9.9626 0 0 9.9626 223.533 223.509 Tm
0 Tc
(.)Tj
-17.1316 -1.3 TD
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[(These)-359.7(r)-0.5(esults,)-366.4(a)0.3(nd)-359.7(a)-359.2(wider)-361(searc)27.9(h)-359.7(for)-360(s)-0.4(mall)-360.1(p)-28.1(o)28.3(w)28.3(e)-0.1(rs)-360.9(of)]TJ
-1.1997 -1.3009 TD
[(small)-358.3(Salem)-359.2(n)27.9(um)28.3(b)-28.1(e)-0.1(rs,)-362.8(a)0.3(re)-357.9(recorded)-357(in)-358.8(T)83.4(a)0.3(ble)-358.8(1)0.3(.)-517.3(O)-0.1(n)-357.9(e)-0.1(ac)27.9(h)]TJ
0 -1.3 TD
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[(line,)-285.2(a)-271.7(list)-272.6(o)0.2(f)-272.8(c)-0.2(yclotomic)-273.9(graphs)-272.5(indicates)-274.3(t)0.2(he)-272.1(comp)-28.2(onen)27.8(ts)]TJ
T*
-0.0004 Tc
(of)Tj
/F6 1 Tf
1.3045 0 TD
0 Tc
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 61.11 175.314 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 68.877 171.696 Tm
-0.0002 Tc
[(in)-499.8(the)-498.9(c)-0.2(onstruction)-500.7(of)-499.6(Theorem)-500.3(7.2\(i\);)-584.2(t)28.2(w)28.2(o)-501.1(lists)]TJ
-2.8077 -1.3 TD
[(separated)-350.7(b)27.8(y)-349.6(a)-350.3(semicolon)-351.6(indicate)-351.6(the)-349.8(c)-0.2(omp)-28.2(onen)27.8(ts)-351.9(of)]TJ
/F6 1 Tf
23.5675 0 TD
0 Tc
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 282.906 162.3631 Tm
()Tj
/F13 1 Tf
-0.1987 -0.8724 TD
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 40.905 145.794 Tm
-0.0002 Tc
(and)Tj
/F6 1 Tf
1.9441 0 TD
0 Tc
(T)Tj
/F15 1 Tf
6.9738 0 0 6.9738 67.482 149.412 Tm
()Tj
/F13 1 Tf
-0.1987 -0.8724 TD
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 73.89 145.794 Tm
-0.0002 Tc
[(in)-333.6(the)-334.5(c)-0.2(onstruction)-334.5(of)-334.2(Theorem)-334(7.2\(ii\).)]TJ
/F3 1 Tf
-3.3109 -2.7887 TD
-0.0003 Tc
[(A)37(CKNO)17.8(W)-0.4(LEDGMENTS)]TJ
/F9 1 Tf
8.9664 0 0 8.9664 40.905 101.0731 Tm
-0.0001 Tc
[(W)85.5(e)-280.7(are)-280.7(v)28.4(ery)-281.7(g)-0.1(rateful)-280.7(to)-281.2(P)27.8(e)0.4(ter)-281.6(R)-0.4(o)28(w)-0.6(linson)-280.3(f)-0.2(or)-281.6(pro)28(viding)-281.2(u)-0.2(s)-280.3(w)-0.6(ith)]TJ
0 -1.2216 TD
[(man)27.9(y)-497.5(references)-499.1(on)-498.1(graph)-497.1(e)0.4(igen)27.9(v)57.5(a)-0.1(lues.)-925.1(W)85.5(e)-498.5(a)-0.1(lso)-498(t)0.1(hank)-498.5(the)]TJ
0 -1.2226 TD
[(referees)-343.5(for)-342.9(h)-0.2(elpful)-343(commen)27.9(t)0.1(s.)]TJ
ET
309.177 713.582 m
543.753 713.582 l
309.379 700.23 m
309.379 713.388 l
S
BT
/F2 1 Tf
9.9626 0 0 9.9626 314.55 704.172 Tm
[(Salem)-334.8(n)27.9(um)28.3(b)-28.1(e)-0.1(r)]TJ
ET
382.027 700.23 m
382.027 713.388 l
S
BT
9.9626 0 0 9.9626 422.1998 704.172 Tm
-0.0002 Tc
[(Cyclotomic)-337.2(graphs)]TJ
ET
543.55 700.23 m
543.55 713.388 l
309.177 700.036 m
543.753 700.036 l
309.379 686.676 m
309.379 699.834 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 341.289 690.6271 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 345.645 689.1331 Tm
(1)Tj
ET
382.027 686.676 m
382.027 699.834 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 450.063 690.6271 Tm
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 458.307 689.1331 Tm
(9)Tj
/F2 1 Tf
9.9626 0 0 9.9626 462.78 690.6271 Tm
-0.0004 Tc
(\(0\))Tj
ET
543.55 686.676 m
543.55 699.834 l
309.379 673.527 m
309.379 686.685 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 677.478 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 681.087 Tm
(2)Tj
-0.1613 -0.8724 TD
(1)Tj
ET
382.027 673.527 m
382.027 686.685 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 443.376 677.478 Tm
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 451.62 675.984 Tm
-0.0003 Tc
(11)Tj
/F2 1 Tf
9.9626 0 0 9.9626 460.062 677.478 Tm
(\(3)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
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/F2 1 Tf
0.4436 0 TD
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(8\))Tj
ET
543.55 673.527 m
543.55 686.685 l
309.379 660.378 m
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S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 664.3201 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 667.938 Tm
(6)Tj
-0.1613 -0.8724 TD
(1)Tj
ET
382.027 660.378 m
382.027 673.536 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 416.322 664.3201 Tm
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 423.675 662.826 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 428.139 664.3201 Tm
-0.0004 Tc
(\(1\))Tj
/F6 1 Tf
1.2765 0 TD
0 Tc
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/F2 1 Tf
0.6793 0.2529 TD
()Tj
/F6 1 Tf
-0.2358 -0.2529 TD
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 453.519 662.826 Tm
(4)Tj
/F2 1 Tf
9.9626 0 0 9.9626 458.019 664.3201 Tm
-0.0004 Tc
(\(0\);)Tj
/F6 1 Tf
1.72 0 TD
0 Tc
(A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 482.625 662.826 Tm
(5)Tj
/F2 1 Tf
9.9626 0 0 9.9626 487.116 664.3201 Tm
-0.0004 Tc
(\(2)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(4\))Tj
ET
543.55 660.378 m
543.55 673.536 l
309.379 647.229 m
309.379 660.387 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 651.171 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 654.7891 Tm
(8)Tj
-0.1613 -0.8737 TD
(1)Tj
ET
382.027 647.229 m
382.027 660.387 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 402.273 651.171 Tm
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 409.626 649.677 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 414.099 651.171 Tm
-0.0004 Tc
(\(1\))Tj
/F6 1 Tf
1.2765 0 TD
0.1658 Tc
(,A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 438.705 649.677 Tm
0 Tc
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 443.196 651.171 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
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(2\);)Tj
/F6 1 Tf
1.3316 0 TD
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(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 477.081 649.677 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 481.59 651.171 Tm
-0.0004 Tc
(\(5\))Tj
/F6 1 Tf
1.2765 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.6766 0.2529 TD
()Tj
/F6 1 Tf
-0.2331 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 506.079 649.677 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 510.57 651.171 Tm
-0.0004 Tc
(\(3\))Tj
ET
543.55 647.229 m
543.55 660.387 l
309.177 647.036 m
543.753 647.036 l
309.379 633.675 m
309.379 646.833 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 637.626 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 641.235 Tm
(2)Tj
-0.1613 -0.8724 TD
(2)Tj
ET
382.027 633.675 m
382.027 646.833 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 436.023 637.626 Tm
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 443.376 636.132 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 447.84 637.626 Tm
-0.0004 Tc
(\(7\);)Tj
/F6 1 Tf
1.72 0 TD
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 472.329 636.132 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 476.829 637.626 Tm
-0.0004 Tc
(\(7\))Tj
ET
543.55 633.675 m
543.55 646.833 l
309.177 633.482 m
543.753 633.482 l
309.379 620.13 m
309.379 633.288 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 624.072 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 627.69 Tm
(2)Tj
-0.1613 -0.8737 TD
(3)Tj
ET
382.027 620.13 m
382.027 633.288 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 436.023 624.072 Tm
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 443.376 622.578 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 447.84 624.072 Tm
-0.0004 Tc
(\(6\);)Tj
/F6 1 Tf
1.72 0 TD
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 472.329 622.578 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 476.829 624.072 Tm
-0.0004 Tc
(\(6\))Tj
ET
543.55 620.13 m
543.55 633.288 l
309.379 606.981 m
309.379 620.139 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 610.923 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 614.541 Tm
(5)Tj
-0.1613 -0.8737 TD
(3)Tj
ET
382.027 606.981 m
382.027 620.139 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 404.865 610.923 Tm
(A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 412.335 609.429 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 416.808 610.923 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(1\))Tj
/F6 1 Tf
0.888 0 TD
0.1658 Tc
(,A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 450.81 609.429 Tm
0 Tc
(9)Tj
/F2 1 Tf
9.9626 0 0 9.9626 455.319 610.923 Tm
-0.0004 Tc
(\(2)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(8\);)Tj
/F6 1 Tf
1.3316 0 TD
0 Tc
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 490.095 609.429 Tm
-0.0003 Tc
(15)Tj
/F2 1 Tf
9.9626 0 0 9.9626 498.573 610.923 Tm
(\(8)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(7\))Tj
ET
543.55 606.981 m
543.55 620.139 l
309.177 606.779 m
543.753 606.779 l
309.379 593.427 m
309.379 606.585 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 597.3781 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 600.9871 Tm
(5)Tj
-0.1613 -0.8724 TD
(4)Tj
ET
382.027 593.427 m
382.027 606.585 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 406.746 597.3781 Tm
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 414.099 595.884 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 418.572 597.3781 Tm
-0.0004 Tc
(\(4\))Tj
/F6 1 Tf
1.2765 0 TD
0.1658 Tc
(,D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 443.952 595.884 Tm
0 Tc
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 448.452 597.3781 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(6\);)Tj
/F6 1 Tf
1.3316 0 TD
0 Tc
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 483.228 595.884 Tm
-0.0003 Tc
(13)Tj
/F2 1 Tf
9.9626 0 0 9.9626 491.706 597.3781 Tm
(\(3)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(10\))Tj
ET
543.55 593.427 m
543.55 606.585 l
309.177 593.234 m
543.753 593.234 l
309.379 579.882 m
309.379 593.04 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 583.824 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 587.442 Tm
(2)Tj
-0.1613 -0.8737 TD
(5)Tj
ET
382.027 579.882 m
382.027 593.04 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 436.023 583.824 Tm
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 443.376 582.33 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 447.84 583.824 Tm
-0.0004 Tc
(\(1\);)Tj
/F6 1 Tf
1.72 0 TD
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 472.329 582.33 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 476.829 583.824 Tm
-0.0004 Tc
(\(1\))Tj
ET
543.55 579.882 m
543.55 593.04 l
309.379 566.733 m
309.379 579.891 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 570.675 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 574.293 Tm
(3)Tj
-0.1613 -0.8737 TD
(5)Tj
ET
382.027 566.733 m
382.027 579.891 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 436.023 570.675 Tm
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 443.376 569.181 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 447.84 570.675 Tm
-0.0004 Tc
(\(1\);)Tj
1.954 0.2529 TD
0 Tc
()Tj
/F6 1 Tf
-0.234 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 472.329 569.181 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 476.829 570.675 Tm
-0.0004 Tc
(\(7\))Tj
ET
543.55 566.733 m
543.55 579.891 l
309.379 553.575 m
309.379 566.733 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 557.526 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 561.135 Tm
(4)Tj
-0.1613 -0.8724 TD
(5)Tj
ET
382.027 553.575 m
382.027 566.733 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 426.393 557.526 Tm
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 433.746 556.032 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 438.219 557.526 Tm
-0.0004 Tc
(\(4\))Tj
/F6 1 Tf
1.2765 0 TD
0.1658 Tc
(,D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 463.599 556.032 Tm
-0.0003 Tc
(18)Tj
/F2 1 Tf
9.9626 0 0 9.9626 472.059 557.526 Tm
(\(12)Tj
/F6 1 Tf
1.3876 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(6\))Tj
ET
543.55 553.575 m
543.55 566.733 l
309.379 540.426 m
309.379 553.584 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 544.377 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 547.986 Tm
(5)Tj
-0.1613 -0.8724 TD
(5)Tj
ET
382.027 540.426 m
382.027 553.584 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 387.207 544.377 Tm
(A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 394.677 542.8831 Tm
(4)Tj
/F2 1 Tf
9.9626 0 0 9.9626 399.15 544.377 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(4\))Tj
/F6 1 Tf
0.888 0 TD
0.1658 Tc
(,A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 433.152 542.8831 Tm
0 Tc
(4)Tj
/F2 1 Tf
9.9626 0 0 9.9626 437.661 544.377 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(4\);)Tj
/F6 1 Tf
1.3316 0 TD
0 Tc
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 472.437 542.8831 Tm
(4)Tj
/F2 1 Tf
9.9626 0 0 9.9626 476.946 544.377 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(3\))Tj
/F6 1 Tf
0.888 0 TD
0.1658 Tc
(,D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 511.722 542.8831 Tm
0 Tc
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 516.231 544.377 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(7\))Tj
ET
543.55 540.426 m
543.55 553.584 l
309.379 527.277 m
309.379 540.435 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 531.219 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 534.837 Tm
(6)Tj
-0.1613 -0.8724 TD
(5)Tj
ET
382.027 527.277 m
382.027 540.435 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 387.207 531.219 Tm
(A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 394.677 529.725 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 399.15 531.219 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(1\))Tj
/F6 1 Tf
0.888 0 TD
0.1658 Tc
(,A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 433.152 529.725 Tm
0 Tc
(3)Tj
/F2 1 Tf
9.9626 0 0 9.9626 437.661 531.219 Tm
-0.0004 Tc
(\(2)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(2\);)Tj
/F6 1 Tf
1.3316 0 TD
0 Tc
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 472.437 529.725 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 476.946 531.219 Tm
-0.0004 Tc
(\(2)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(4\))Tj
/F6 1 Tf
0.888 0 TD
0.1658 Tc
(,D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 511.722 529.725 Tm
0 Tc
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 516.231 531.219 Tm
-0.0004 Tc
(\(4)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(4\))Tj
ET
543.55 527.277 m
543.55 540.435 l
309.177 527.083 m
543.753 527.083 l
309.379 513.732 m
309.379 526.89 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 341.289 517.674 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 345.645 516.1801 Tm
(7)Tj
ET
382.027 513.732 m
382.027 526.89 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 448.074 517.674 Tm
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 456.318 516.1801 Tm
-0.0003 Tc
(10)Tj
/F2 1 Tf
9.9626 0 0 9.9626 464.769 517.674 Tm
(\(0\))Tj
ET
543.55 513.732 m
543.55 526.89 l
309.379 500.574 m
309.379 513.732 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 504.525 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 508.134 Tm
(4)Tj
-0.1613 -0.8724 TD
(7)Tj
ET
382.027 500.574 m
382.027 513.732 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 397.512 504.525 Tm
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 404.865 503.031 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 409.338 504.525 Tm
-0.0004 Tc
(\(1\))Tj
/F6 1 Tf
1.2765 0 TD
0.1658 Tc
(,A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 433.944 503.031 Tm
0 Tc
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 438.435 504.525 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(1\);)Tj
/F6 1 Tf
1.3316 0 TD
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 472.32 503.031 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 476.829 504.525 Tm
-0.0004 Tc
(\(1\))Tj
/F6 1 Tf
1.2765 0 TD
0.1658 Tc
(,A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 501.435 503.031 Tm
0 Tc
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 505.926 504.525 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(1\))Tj
ET
543.55 500.574 m
543.55 513.732 l
309.379 487.425 m
309.379 500.583 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 491.367 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 494.985 Tm
(5)Tj
-0.1613 -0.8724 TD
(7)Tj
ET
382.027 487.425 m
382.027 500.583 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 404.478 491.367 Tm
(A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 411.948 489.873 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 416.421 491.367 Tm
-0.0004 Tc
(\(2)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(6\);)Tj
/F6 1 Tf
1.3316 0 TD
0 Tc
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 451.197 489.873 Tm
(4)Tj
/F2 1 Tf
9.9626 0 0 9.9626 455.706 491.367 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(3\))Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.6802 0.2529 TD
()Tj
/F6 1 Tf
-0.2367 -0.2529 TD
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 490.482 489.873 Tm
-0.0003 Tc
(10)Tj
/F2 1 Tf
9.9626 0 0 9.9626 498.96 491.367 Tm
(\(5)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(5\))Tj
ET
543.55 487.425 m
543.55 500.583 l
309.379 474.276 m
309.379 487.434 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 340.722 478.218 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 346.203 481.836 Tm
(6)Tj
-0.1613 -0.8724 TD
(7)Tj
ET
382.027 474.276 m
382.027 487.434 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 411.228 478.218 Tm
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 418.581 476.724 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 423.045 478.218 Tm
-0.0004 Tc
(\(3\))Tj
/F6 1 Tf
1.2765 0 TD
0.1658 Tc
(,D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 448.425 476.724 Tm
0 Tc
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 452.925 478.218 Tm
-0.0004 Tc
(\(4)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(3\);)Tj
/F6 1 Tf
1.3316 0 TD
0 Tc
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 487.701 476.724 Tm
(9)Tj
/F2 1 Tf
9.9626 0 0 9.9626 492.21 478.218 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(8\))Tj
ET
543.55 474.276 m
543.55 487.434 l
309.177 474.083 m
543.753 474.083 l
309.379 460.722 m
309.379 473.88 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 464.673 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 468.291 Tm
(3)Tj
-0.1613 -0.8737 TD
-0.0003 Tc
(10)Tj
ET
382.027 460.722 m
382.027 473.88 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 435.573 464.673 Tm
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 442.926 463.179 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 447.399 464.673 Tm
-0.0004 Tc
(\(8\);)Tj
/F6 1 Tf
1.72 0 TD
0 Tc
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 472.779 463.179 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 477.27 464.673 Tm
-0.0004 Tc
(\(0\))Tj
ET
543.55 460.722 m
543.55 473.88 l
309.177 460.529 m
543.753 460.529 l
309.379 447.177 m
309.379 460.335 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 451.119 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 454.737 Tm
(2)Tj
-0.1613 -0.8724 TD
-0.0003 Tc
(12)Tj
ET
382.027 447.177 m
382.027 460.335 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 435.123 451.119 Tm
0 Tc
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 443.367 449.6251 Tm
(5)Tj
/F2 1 Tf
9.9626 0 0 9.9626 447.84 451.119 Tm
-0.0004 Tc
(\(0\);)Tj
/F6 1 Tf
1.72 0 TD
0 Tc
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 473.22 449.6251 Tm
(5)Tj
/F2 1 Tf
9.9626 0 0 9.9626 477.72 451.119 Tm
-0.0004 Tc
(\(0\))Tj
ET
543.55 447.177 m
543.55 460.335 l
309.379 434.028 m
309.379 447.186 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 437.97 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 441.588 Tm
(3)Tj
-0.1613 -0.8737 TD
-0.0003 Tc
(12)Tj
ET
382.027 434.028 m
382.027 447.186 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 436.023 437.97 Tm
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 443.376 436.476 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 447.84 437.97 Tm
-0.0004 Tc
(\(5\);)Tj
/F6 1 Tf
1.72 0 TD
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 472.329 436.476 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 476.829 437.97 Tm
-0.0004 Tc
(\(6\))Tj
ET
543.55 434.028 m
543.55 447.186 l
309.379 420.879 m
309.379 434.037 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 424.821 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 428.439 Tm
(5)Tj
-0.1613 -0.8737 TD
-0.0003 Tc
(12)Tj
ET
382.027 420.879 m
382.027 434.037 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 416.763 424.821 Tm
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 424.116 423.327 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 428.589 424.821 Tm
-0.0004 Tc
(\(4\))Tj
/F6 1 Tf
1.2765 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.6766 0.2529 TD
()Tj
/F6 1 Tf
-0.2331 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 453.078 423.327 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 457.569 424.821 Tm
-0.0004 Tc
(\(1\);)Tj
/F6 1 Tf
1.7201 0 TD
0 Tc
(A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 482.175 423.327 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 486.666 424.821 Tm
-0.0004 Tc
(\(3)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(5\))Tj
ET
543.55 420.879 m
543.55 434.037 l
309.177 420.677 m
543.753 420.677 l
309.379 407.325 m
309.379 420.483 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 411.267 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 414.885 Tm
(2)Tj
-0.1613 -0.8724 TD
-0.0003 Tc
(15)Tj
ET
382.027 407.325 m
382.027 420.483 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 440.883 411.267 Tm
0 Tc
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 449.127 409.773 Tm
-0.0003 Tc
(18)Tj
/F2 1 Tf
9.9626 0 0 9.9626 457.569 411.267 Tm
(\(6)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(12\))Tj
ET
543.55 407.325 m
543.55 420.483 l
309.379 394.176 m
309.379 407.334 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 398.118 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 401.736 Tm
(4)Tj
-0.1613 -0.8724 TD
-0.0003 Tc
(15)Tj
ET
382.027 394.176 m
382.027 407.334 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 392.643 398.118 Tm
0 Tc
(A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 400.113 396.624 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 404.586 398.118 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(1\))Tj
/F6 1 Tf
0.888 0 TD
0.1658 Tc
(,D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 439.362 396.624 Tm
-0.0003 Tc
(10)Tj
/F2 1 Tf
9.9626 0 0 9.9626 447.84 398.118 Tm
(\(0\);)Tj
/F6 1 Tf
1.72 0 TD
0 Tc
(A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 472.446 396.624 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 476.946 398.118 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(1\))Tj
/F6 1 Tf
0.888 0 TD
0.1658 Tc
(,D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 511.722 396.624 Tm
-0.0003 Tc
(10)Tj
/F2 1 Tf
9.9626 0 0 9.9626 520.2 398.118 Tm
(\(0\))Tj
ET
543.55 394.176 m
543.55 407.334 l
309.177 393.983 m
543.753 393.983 l
309.379 380.622 m
309.379 393.78 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 384.573 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 388.191 Tm
(4)Tj
-0.1613 -0.8737 TD
-0.0003 Tc
(16)Tj
ET
382.027 380.622 m
382.027 393.78 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 411.228 384.573 Tm
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 418.581 383.079 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 423.045 384.573 Tm
-0.0004 Tc
(\(1\))Tj
/F6 1 Tf
1.2765 0 TD
0.1658 Tc
(,D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 448.425 383.079 Tm
0 Tc
(9)Tj
/F2 1 Tf
9.9626 0 0 9.9626 452.925 384.573 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(8\))Tj
/F6 1 Tf
0.888 0 TD
0.1658 Tc
(,D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 487.701 383.079 Tm
0 Tc
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 492.21 384.573 Tm
-0.0004 Tc
(\(2)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(6\))Tj
ET
543.55 380.622 m
543.55 393.78 l
309.177 380.429 m
543.753 380.429 l
309.379 367.077 m
309.379 380.235 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 371.019 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 343.656 369.5251 Tm
-0.0003 Tc
(19)Tj
ET
382.027 367.077 m
382.027 380.235 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 448.074 371.019 Tm
0 Tc
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 456.318 369.5251 Tm
-0.0003 Tc
(11)Tj
/F2 1 Tf
9.9626 0 0 9.9626 464.769 371.019 Tm
(\(0\))Tj
ET
543.55 367.077 m
543.55 380.235 l
309.379 353.928 m
309.379 367.086 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 357.8701 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 361.488 Tm
(3)Tj
-0.1613 -0.8737 TD
-0.0003 Tc
(19)Tj
ET
382.027 353.928 m
382.027 367.086 l
S
BT
/F2 1 Tf
9.9626 0 0 9.9626 433.17 360.39 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 438.219 356.376 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 442.692 357.8701 Tm
-0.0004 Tc
(\(8\);)Tj
/F6 1 Tf
1.72 0 TD
0 Tc
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 468.072 356.376 Tm
(4)Tj
/F2 1 Tf
9.9626 0 0 9.9626 472.563 357.8701 Tm
-0.0004 Tc
(\(2)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(2\))Tj
ET
543.55 353.928 m
543.55 367.086 l
309.379 340.779 m
309.379 353.937 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 344.721 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 348.3391 Tm
(4)Tj
-0.1613 -0.8737 TD
-0.0003 Tc
(19)Tj
ET
382.027 340.779 m
382.027 353.937 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 397.512 344.721 Tm
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 404.865 343.227 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 409.338 344.721 Tm
-0.0004 Tc
(\(4\))Tj
/F6 1 Tf
1.2765 0 TD
0.1658 Tc
(,A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 433.944 343.227 Tm
0 Tc
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 438.435 344.721 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(1\);)Tj
/F6 1 Tf
1.3316 0 TD
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 472.32 343.227 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 476.829 344.721 Tm
-0.0004 Tc
(\(4\))Tj
/F6 1 Tf
1.2765 0 TD
0.1658 Tc
(,A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 501.435 343.227 Tm
0 Tc
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 505.926 344.721 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(1\))Tj
ET
543.55 340.779 m
543.55 353.937 l
309.379 327.621 m
309.379 340.779 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 331.572 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 335.181 Tm
(5)Tj
-0.1613 -0.8724 TD
-0.0003 Tc
(19)Tj
ET
382.027 327.621 m
382.027 340.779 l
S
BT
/F2 1 Tf
9.9626 0 0 9.9626 394.668 334.092 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 399.717 330.078 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 404.181 331.572 Tm
-0.0004 Tc
(\(2\))Tj
/F6 1 Tf
1.2765 0 TD
0.1658 Tc
(,A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 428.787 330.078 Tm
0 Tc
(3)Tj
/F2 1 Tf
9.9626 0 0 9.9626 433.287 331.572 Tm
-0.0004 Tc
(\(2)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(2\);)Tj
/F6 1 Tf
1.3316 0 TD
0 Tc
(A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 467.289 330.078 Tm
(3)Tj
/F2 1 Tf
9.9626 0 0 9.9626 471.789 331.572 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(3\))Tj
/F6 1 Tf
0.888 0 TD
0.1658 Tc
(,D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 506.565 330.078 Tm
0 Tc
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 511.074 331.572 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(5\))Tj
ET
543.55 327.621 m
543.55 340.779 l
309.177 327.428 m
543.753 327.428 l
309.379 314.076 m
309.379 327.234 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 318.018 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 321.636 Tm
(2)Tj
-0.1613 -0.8724 TD
-0.0003 Tc
(21)Tj
ET
382.027 314.076 m
382.027 327.234 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 436.023 318.018 Tm
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 443.376 316.524 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 447.84 318.018 Tm
-0.0004 Tc
(\(1\);)Tj
/F6 1 Tf
1.72 0 TD
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 472.329 316.524 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 476.829 318.018 Tm
-0.0004 Tc
(\(1\))Tj
ET
543.55 314.076 m
543.55 327.234 l
309.379 300.927 m
309.379 314.085 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 304.869 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 308.487 Tm
(5)Tj
-0.1613 -0.8737 TD
-0.0003 Tc
(21)Tj
ET
382.027 300.927 m
382.027 314.085 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 412.002 304.869 Tm
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 419.355 303.375 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 423.828 304.869 Tm
-0.0004 Tc
(\(3\))Tj
/F6 1 Tf
1.2765 0 TD
0.1658 Tc
(,A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 448.434 303.375 Tm
0 Tc
(4)Tj
/F2 1 Tf
9.9626 0 0 9.9626 452.925 304.869 Tm
-0.0004 Tc
(\(2)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(3\);)Tj
/F6 1 Tf
1.3316 0 TD
0 Tc
(A)Tj
/F13 1 Tf
6.9738 0 0 6.9738 486.927 303.375 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 491.436 304.869 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(6\))Tj
ET
543.55 300.927 m
543.55 314.085 l
309.177 300.725 m
543.753 300.725 l
309.379 287.373 m
309.379 300.531 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 291.324 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 343.656 289.83 Tm
-0.0003 Tc
(23)Tj
ET
382.027 287.373 m
382.027 300.531 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 450.513 291.324 Tm
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 457.866 289.83 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 462.33 291.324 Tm
-0.0004 Tc
(\(1\))Tj
ET
543.55 287.373 m
543.55 300.531 l
309.379 274.224 m
309.379 287.382 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 278.166 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 281.784 Tm
(2)Tj
-0.1613 -0.8724 TD
-0.0003 Tc
(23)Tj
ET
382.027 274.224 m
382.027 287.382 l
S
BT
/F2 1 Tf
9.9626 0 0 9.9626 452.817 280.686 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 457.866 276.6721 Tm
(8)Tj
/F2 1 Tf
9.9626 0 0 9.9626 462.33 278.166 Tm
-0.0004 Tc
(\(6\))Tj
ET
543.55 274.224 m
543.55 287.382 l
309.379 261.075 m
309.379 274.233 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 265.017 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 268.635 Tm
(3)Tj
-0.1613 -0.8737 TD
-0.0003 Tc
(23)Tj
ET
382.027 261.075 m
382.027 274.233 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 430.866 265.017 Tm
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 438.219 263.523 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 442.692 265.017 Tm
-0.0004 Tc
(\(2\);)Tj
/F6 1 Tf
1.72 0 TD
0 Tc
(D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 468.072 263.523 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 472.563 265.017 Tm
-0.0004 Tc
(\(1)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(5\))Tj
ET
543.55 261.075 m
543.55 274.233 l
309.379 247.926 m
309.379 261.084 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 251.868 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 255.486 Tm
(4)Tj
-0.1613 -0.8737 TD
-0.0003 Tc
(23)Tj
ET
382.027 247.926 m
382.027 261.084 l
S
BT
/F2 1 Tf
9.9626 0 0 9.9626 431.19 254.388 Tm
0 Tc
()Tj
/F6 1 Tf
-0.2313 -0.2529 TD
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 436.239 250.374 Tm
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 440.703 251.868 Tm
-0.0004 Tc
(\(3\))Tj
/F6 1 Tf
1.2765 0 TD
0.1658 Tc
(,D)Tj
/F13 1 Tf
6.9738 0 0 6.9738 466.083 250.374 Tm
-0.0003 Tc
(12)Tj
/F2 1 Tf
9.9626 0 0 9.9626 474.552 251.868 Tm
(\(9)Tj
/F6 1 Tf
0.888 0 TD
0 Tc
(,)Tj
/F2 1 Tf
0.4436 0 TD
-0.0004 Tc
(3\))Tj
ET
543.55 247.926 m
543.55 261.084 l
309.177 247.724 m
543.753 247.724 l
309.379 234.372 m
309.379 247.53 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 339.3 238.323 Tm
0 Tc
()Tj
/F13 1 Tf
6.9738 0 0 6.9738 344.781 241.9321 Tm
(4)Tj
-0.1613 -0.8724 TD
-0.0003 Tc
(35)Tj
ET
382.027 234.372 m
382.027 247.53 l
S
BT
/F6 1 Tf
9.9626 0 0 9.9626 397.512 238.323 Tm
0 Tc
(E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 404.865 236.829 Tm
(6)Tj
/F2 1 Tf
9.9626 0 0 9.9626 409.338 238.323 Tm
-0.0004 Tc
(\(4\))Tj
/F6 1 Tf
1.2765 0 TD
0.1658 Tc
(,E)Tj
/F13 1 Tf
6.9738 0 0 6.9738 433.827 236.829 Tm
0 Tc
(7)Tj
/F2 1 Tf
9.9626 0 0 9.9626 438.318 238.323 Tm
-0.0004 Tc
(\(1\);)Tj
/F6 1 Tf
1.72 0 TD
0 Tc
(A)Tj
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