Geodesic
Cycle structure of the elements of centralizers of permutations from the symmetric group
Matematičeskie voprosy kriptografii, Tome 1 (2010) no. 1, pp. 85-100 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\xi$ be the number of cycles of a random element of centralizer of a permutation from the symmetric group $S_n$ with given cycle structure. For some classes of permutations generating functions and limit distributions of $\xi$ as $n\to\infty$ are described. 
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V. N. Sachkov. Cycle structure of the elements of centralizers of permutations from the symmetric group. Matematičeskie voprosy kriptografii, Tome 1 (2010) no. 1, pp. 85-100. http://geodesic.mathdoc.fr/item/MVK_2010_1_1_a4/

[1] Sachkov V. N., “Translyatory i translyatsii diskretnykh funktsii”, Trudy po diskretnoi matematike, 9, Gelios, M., 2006, 253–268

[2] Sachkov V. N., Kombinatornye metody diskretnoi matematiki, Nauka, M., 1977