Using recurrence relations to count certain elements in symmetric groups

Authors

Stephen P. Glasby, Central Washington University

Document Type

Article

Department or Administrative Unit

Mathematics

Publication Date

5-2001

Abstract

We use the fact that certain cosets of the stabilizer of points are pairwise conjugate in a symmetric group S_n in order to construct recurrence relations for enumerating certain subsets of S_n. Occasionally one can find ‘closed form’ solutions to such recurrence relations. For example, the probability that a random element of S_n has no cycle of length divisible by q is ∏_{d = 1}^{⌊n / q⌋}(1 − 1dq).

Comments

This article was originally published in European Journal of Combinatorics. The full-text article from the publisher can be found here.

Due to copyright restrictions, this article is not available for free download from ScholarWorks @ CWU.

Recommended Citation

Glasby, S. P. (2001). Using Recurrence Relations to Count Certain Elements in Symmetric Groups. European Journal of Combinatorics, 22(4), 497–501. https://doi.org/10.1006/eujc.2001.0500

Journal

European Journal of Combinatorics

Copyright

© 2001 Academic Press