Abstract
The power group method of de Bruijn and Harary in enumeration under group action of mappings between finite sets is extended to include correlation of group actions on domain and range. By relaxing the restriction of weight functions to be constant over orbits, more specific results concerning the enumeration of orbits by weight are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Pólya, G.: Acta Math. 68, 145 (1937)
de Bruijn, N. G.: Indag. Math. 21, 59 (1959)
Harary, F., Palmer, E.: J. Comb. Theory 1, 157 (1966)
Harary, F.: Am. math. Monthly 66, 572 (1959)
Neumann, P. M.: Math. Scientist 4, 133 (1979)
de Bruijn, N. G.: in Applied combinatorical mathematics, pp. 744, E. F. Beckenbach, ed. New York: Wiley 1964
Harary, F., Palmer, E.: Graphical enumeration, New York: Academic Press, 1973
Kerber, A.: Representations of permutation groups II, Lecture Notes in Mathematics, Vol. 495. Berlin: Springer Verlag 1975
Kerber, A., in The permutation group in physics and chemistry, pp. 1, Lecture Notes in Chemistry, Vol. 12. Berlin: Springer Verlag 1979
Davidson, R. A.: Ph.D. Thesis, The Pennsylvania State University, 1977
de Bruijn, N. G.: J. Comb. Theory 2, 418 (1967)
Hässelbarth, W., Ruch, E.: Israel J. Chem. 15, 112 (1977)
Hässelbarth, W., Ruch, E., Klein, D. J., Seligman, T. H.: J. Math. Phys. 21, 951 (1980)
Ruch, E., Klein, D. J.: Theoret. Chim. Acta (Berl.) 63, 447 (1983)
Ruch, E., Hässelbarth, W., Richter, B.: Theoret. Chim. Acta (Berl.) 19, 288 (1970)
Author information
Authors and Affiliations
Additional information
This paper is dedicated to Professor Dr. Ernst Ruch on the occasion of this 65th birthday
Rights and permissions
About this article
Cite this article
Hässelbarth, W. A note on pólya enumeration theory. Theoret. Chim. Acta 66, 91–110 (1984). https://doi.org/10.1007/BF00551111
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00551111