Geodesic
Asymptotics of the Moments of the Number of Cycles of a Random $A$-Permutation
Matematičeskie zametki, Tome 88 (2010) no. 5, pp. 792-800

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We consider random permutations uniformly distributed on the set of all permutations of degree $n$ whose cycle lengths belong to a fixed set $A$ (the so-called $A$-permutations). In the present paper, we establish an asymptotics of the moments of the total number of cycles and of the number of cycles of given length of this random permutation as $n\to\infty$.
Keywords: random $A$-permutation, number of cycles of a permutation, uniform distribution, moments of the total number of cycles, slowly varying function. 
@article{MZM_2010_88_5_a13,
     author = {A. L. Yakymiv},
     title = {Asymptotics of the {Moments} of the {Number} of {Cycles} of a {Random} $A${-Permutation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {792--800},
     publisher = {mathdoc},
     volume = {88},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_5_a13/}
}
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A. L. Yakymiv. Asymptotics of the Moments of the Number of Cycles of a Random $A$-Permutation. Matematičeskie zametki, Tome 88 (2010) no. 5, pp. 792-800. http://geodesic.mathdoc.fr/item/MZM_2010_88_5_a13/