Acta Mathematica

Enumeration under two representations of the wreath product

E. M. Palmer and R. W. Robinson

Full-text: Open access

Note

The authors would like to thank Professor Frank Harary for encouraging the research for this paper and for offering many helpful suggestions.

Note

Work supported in part by a grant from the National Science Foundation.

Note

Work supported in part by a grant (73-2502) from the US Air Force Office of Scientific Research.

Article information

Source
Acta Math., Volume 131 (1973), 123-143.

Dates
Received: 23 October 1972
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485889789

Digital Object Identifier
doi:10.1007/BF02392038

Mathematical Reviews number (MathSciNet)
MR409266

Zentralblatt MATH identifier
0264.05119

Rights
1973 © Almqvist & Wiksell

Citation

Palmer, E. M.; Robinson, R. W. Enumeration under two representations of the wreath product. Acta Math. 131 (1973), 123--143. doi:10.1007/BF02392038. https://projecteuclid.org/euclid.acta/1485889789


Export citation

References

  • Burnside, W., Theory of Groups of Finite Order. Second edition, Cambridge, 1911; reprinted New York, 1955; p. 191.
  • Harary, F., On the number of bi-colored graphs. Pacific J. Math., 8 (1958), 743–755.
  • —, Exponentiation of permutation groups. Amer. Math. Monthly, 66 (1959), 572–575.
  • —, Graph Theory, Addison-Wesley, Reading, 1969.
  • Harary, F. & Palmer, E. M., Graphical Enumeration. Academic Press, New York, 1973.
  • Harrison, M. A. & High, R. G., On the cycle index of a product of permutation groups. J. Combinatorial Theory, 3 (1968), 1–23.
  • Palmer, E. M., The exponentiation group as the automorphism group of a graph. Proof Techniques in Graph Theory (F. Harary, ed.) Academic Press, New York (1969), 125–131.
  • Palmer, E. M. & Robinson, R. W., The matrix group of two permutation groups. Bull. Amer. Math. Soc., 73 (1967), 204–207.
  • Pólya, G., Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen. Acta Math., 68 (1937), 145–253.
  • —, Sur les types des propositions composées, J. Symbolic Logic, 5 (1940), 98–103.
  • Read, R. C., The enumeration of locally restricted graphs I, and II. J. London Math. Soc., 34 (1959), 417–436, and 35 (1960), 344–351.
  • Redfield, J. H., The theory of group-reduced distributions. Amer. J. Math., 49 (1927), 433–455.
  • Robinson, R. W., Enumeration of colored graphs, J. Combinatorial Theory, 4 (1968), 181–190.
  • —, Enumeration of non-separable graphs. J. Combinatorial Theory, 9 (1970), 327–356.
  • Sabidussi, G., Graph multiplication. Math. Z., 72 (1960), 446–457.
  • Slepian, D., On the number of symmetry types of boolean functions of n variables. Canad. J. Math., 5 (1953), 185–193.