Pacific Journal of Mathematics

Enumeration of self-dual configurations.

E. M. Palmer and R. W. Robinson

Article information

Pacific J. Math., Volume 110, Number 1 (1984), 203-221.

First available in Project Euclid: 8 December 2004

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C30: Enumeration in graph theory
Secondary: 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 05C15: Coloring of graphs and hypergraphs 06E30: Boolean functions [See also 94C10] 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX]


Palmer, E. M.; Robinson, R. W. Enumeration of self-dual configurations. Pacific J. Math. 110 (1984), no. 1, 203--221.

Export citation


  • [1] A. E. Brouwer, The enumeration of locally transitive tournaments, Report ZW 138/80, Mathematisch Centrum, Amsterdam (1980).
  • [2] N. G. de Bruijn, Plya's Theory of Counting, Applied Combinatorial Mathematics (E. F. Beckenbach, ed.), Wiley, New York (1964), 144-184.
  • [3] N. G. de Bruijn, Colourpatterns which are invariant under a given permutation of the colours,J. Combinatorial Theory, 2 (1967), 418-421. * Computer programming for the reported data was performed by A. Nymeyer. The second author is grateful to the Australian Research Grants Committee for its financial support, which provided technical assistance and some of the computing equipment.
  • [4] S. W. Golomb,Shift Register Sequences, Holden-Day,San Francisco (1967).
  • [5] F. Harary and E. M. Palmer, Graphical Enumeration, Academic, New York (1973).
  • [6] M. A. Harrison, The number of equivalence classes of booleanfunctions under groups containing negation, IEEE Trans. Electronic Computers EC-12 (1963), 559-561.
  • [7] M. A. Harrison and R. G. High, On the cycle index of a product of permutation groups, J. Combinatorial Theory, 3 (1968), 1-23.
  • [8] O. Knop, E. M. Palmer and R. W. Robinson, Arrangements of point charges having zero electricfield gradient, Acta Cryst. Sect. A, 31 (1975), 19-31.
  • [9] E. M. Palmer and R. W. Robinson, Enumeration under two representations of the wreathproduct, Acta Math., 131 (1973), 123-143.
  • [10] E. M. Palmer and A. J. Schwenk, The number of self-complementary, archiral necklaces, J. Graph Theory, 1 (1977), 309-315.
  • [11] G. Plya, Sur les types des propositions composees, J. Symbolic Logic, 5 (1940), 98-103.
  • [12] G. Plya, Kombinatorische Anzahlbestimmungen fur Gruppen, Graphen und chemische Verbindungen, Acta Math.,68 (1937), 145-254.
  • [13] R. C. Read, On the number of self-complementary graphs and digraphs, J. London Math. Soc, 38 (1963), 99-104.
  • [14] J. H. Redfield, The theory of group-reduceddistributions, Amer. J. Math., 49 (1927), 433-435.
  • [15] D. Slepian, On the number of symmetry types of boolean functions of n variables, Canad. J. Math., 5 (1953), 185-193.