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 Mat. Sb. (N.S.), 1975, Volume 96(138), Number 4, Pages 594–600 (Mi msb3412)

On the cycle structure of random permutations

V. E. Tarakanov, V. P. Chistyakov

Abstract: Suppose a probability distribution is given on the set $S_n$ of all permutations of degree $n$. The authors solve the problem of the joint distribution of the random variables $\alpha_1,…,\alpha_s$, where $\alpha_i$ is the number of cycles of length $i$ in a permutation from $S_n$, in a series of cases, when the initial distribution is not uniform on all of $S_n$ but on certain special subsets of it. In these cases it is shown that in the limit as $n\to\infty$ the random variables $\alpha_1,…,\alpha_s$ are independent and each of them has a Poisson distribution. Cases in which no joint limit distribution exists are also noted.
Bibliography: 4 titles.

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English version:
Mathematics of the USSR-Sbornik, 1975, 25:4, 559–565

Bibliographic databases:

UDC: 519.2

Citation: V. E. Tarakanov, V. P. Chistyakov, “On the cycle structure of random permutations”, Mat. Sb. (N.S.), 96(138):4 (1975), 594–600; Math. USSR-Sb., 25:4 (1975), 559–565

Citation in format AMSBIB
\Bibitem{TarChi75} \by V.~E.~Tarakanov, V.~P.~Chistyakov \paper On~the cycle structure of random permutations \jour Mat. Sb. (N.S.) \yr 1975 \vol 96(138) \issue 4 \pages 594--600 \mathnet{http://mi.mathnet.ru/msb3412} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=380926} \zmath{https://zbmath.org/?q=an:0324.60017} \transl \jour Math. USSR-Sb. \yr 1975 \vol 25 \issue 4 \pages 559--565 \crossref{https://doi.org/10.1070/SM1975v025n04ABEH002463} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Yu. V. Bolotnikov, V. N. Sachkov, V. E. Tarakanov, “Asymptotic normality of some variables connected with the cyclic structure of random permutations”, Math. USSR-Sb., 28:1 (1976), 107–117
2. Yu. V. Bolotnikov, V. N. Sachkov, V. E. Tarakanov, “On some classes of random variables on cycles of permutations”, Math. USSR-Sb., 36:1 (1980), 87–99
3. A. N. Timashev, “On the distribution of the number of cycles of a given length in the class of permutations with known number of cycles”, Discrete Math. Appl., 11:5 (2001), 471–483
4. A. L. Yakymiv, “On the distribution of the $m$th maximal cycle lengths of random $A$-permutations”, Discrete Math. Appl., 15:5 (2005), 527–546
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