Regular Article
Using Recurrence Relations to Count Certain Elements in Symmetric Groups

https://doi.org/10.1006/eujc.2001.0500Get rights and content
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Abstract

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

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