Pacific Journal of Mathematics

Extremal problems on nonaveraging and nondividing sets.

H. L. Abbott

Article information

Pacific J. Math., Volume 91, Number 1 (1980), 1-12.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 10A05
Secondary: 10A21


Abbott, H. L. Extremal problems on nonaveraging and nondividing sets. Pacific J. Math. 91 (1980), no. 1, 1--12.

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  • [1] H. L. Abbott, On a conjecture of Erdos and Straus on non-averaging sets of integers, Proceedings of the Fifth British Combinatorial Conference, (to appear).
  • [2] H. L. Abbott, A. C. Liu and J. Riddell, On sets of integers not containing arithmetic progressions of prescribed length, J. Australian Math. Soc, 28 (1974), 188-193.
  • [3] F. A. Behrend, On sets of integers which contain no three terms in arithmetical progression, Proc. Nat. Acad. Sci. U.S.A., 32 (1946), 331-332.
  • [4] P. Erdos and E. G. Straus, Non-averaging sets II, Combinatorial Theory and its Applications, Vol. II, Colloquia Mathematica Societatis Janos Bolyai, 4 (1970), 405-411.
  • [5] M. N. Huxley, The Distribution of Prime Numbers, Oxford Mathematical Mono- graphs, Part IV.
  • [6] G.G. Lorentz, On a problem in additive number theory, Proc. Amer. Math. Soc, 5 (1954), 838-841.
  • [7] L. Moser, On a theorem of van der Waerden, Canad. Math. Bull., 3 (1960), 23-25.
  • [8] J Riddell, On sets of integers containing no I terms in arithmetic progression, Neiuw. Arch, voor Wisk., (3), 17 (1969), 204-209.
  • [9] J. Spencer, Puncture sets, J. Combinatorial Theory, A17 (1974), 329-336.
  • [10] S. K. Stein, Two combinatorial covering theorems, J. Combinatorial Theory, A16 (1974), 391-397.
  • [11] E. G. Straus, Non-averaging sets, Proceedings of Symposia in Pure Mathematics, Vol. XIX, American Mathematical Society, (1971), 215-222.
  • [12] E. Szemeredi, On a conjecture of Erdos and Heilbronn, Acta Arithmetica, 17 (1970), 227-229.