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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Combinatorial structures and group invariant partitions


Authors: Dennis E. White and S. G. Williamson
Journal: Proc. Amer. Math. Soc. 55 (1976), 233-236
MathSciNet review: 0392600
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Abstract | References | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] W. Burnside, Theory of groups of finite order, Dover Publications, Inc., New York, 1955. 2d ed. MR 0069818
  • [2] Jay P. Fillmore and S. G. Williamson, On backtracking: a combinatorial description of the algorithm, SIAM J. Comput. 3 (1974), 41–55. MR 0362987
  • [3] M. J. Klass, Enumeration of partition classes induced by permutation groups, Ph.D. Dissertation, Department of Mathematics, UCLA, 1972.
  • [4] Dennis E. White, Classifying patterns by automorphism group: an operator theoretic approach, Discrete Math. 13 (1975), no. 3, 277–295. MR 0401493


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0392600-9
Keywords: Partitions, group-invariant partitions, group actions, marks of a group, labeled rooted trees, permutations
Article copyright: © Copyright 1976 American Mathematical Society