Using recurrence relations to count certain elements in symmetric groups
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We use the fact that certain cosets of the stabilizer of points are pairwise conjugate in a symmetric group Sn in order to construct recurrence relations for enumerating certain subsets of Sn. Occasionally one can find ‘closed form’ solutions to such recurrence relations. For example, the probability that a random element of Sn has no cycle of length divisible by q is ∏d = 1⌊n / q⌋(1 − 1dq).
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
European Journal of Combinatorics
© 2001 Academic Press