Combinatorial structures and group invariant partitions
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- by Dennis E. White and S. G. Williamson PDF
- Proc. Amer. Math. Soc. 55 (1976), 233-236 Request permission
Abstract:
If a group acts on a set, an action of the group is induced on the partitions of the set. A formula is developed for the number of partitions invariant under this action. The formula is extended to count combinatorial objects such as labeled rooted trees or permutations defined on the invariant partitions.References
- W. Burnside, Theory of groups of finite order, Dover Publications, Inc., New York, 1955. 2d ed. MR 0069818
- Jay P. Fillmore and S. G. Williamson, On backtracking: a combinatorial description of the algorithm, SIAM J. Comput. 3 (1974), 41–55. MR 362987, DOI 10.1137/0203004 M. J. Klass, Enumeration of partition classes induced by permutation groups, Ph.D. Dissertation, Department of Mathematics, UCLA, 1972.
- Dennis E. White, Classifying patterns by automorphism group: an operator theoretic approach, Discrete Math. 13 (1975), no. 3, 277–295. MR 401493, DOI 10.1016/0012-365X(75)90024-2
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 55 (1976), 233-236
- DOI: https://doi.org/10.1090/S0002-9939-1976-0392600-9
- MathSciNet review: 0392600