Geodesic
Asymptotics with remainder term for moments of the total cycle number of random $A$-permutation
Diskretnaya Matematika, Tome 31 (2019) no. 3, pp. 114-127

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We consider the set of $n$-permutations with cycle lengths belonging to some fixed set $A$ of natural numbers (so-called $A$-permutations). Let random permutation $\tau_n$ be uniformly distributed on this set. For some class of sets $A$ we find the asymptotics with remainder term for moments of total cycle number of $\tau_n$.
Keywords: random $A$-permutations, the total number of cycles, the number of cycles of fixed length. 
@article{DM_2019_31_3_a7,
     author = {A. L. Yakymiv},
     title = {Asymptotics with remainder term for moments of the total cycle number of random $A$-permutation},
     journal = {Diskretnaya Matematika},
     pages = {114--127},
     publisher = {mathdoc},
     volume = {31},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2019_31_3_a7/}
}
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A. L. Yakymiv. Asymptotics with remainder term for moments of the total cycle number of random $A$-permutation. Diskretnaya Matematika, Tome 31 (2019) no. 3, pp. 114-127. http://geodesic.mathdoc.fr/item/DM_2019_31_3_a7/