This article is cited in 4 scientific papers (total in 4 papers)
On the cycle structure of random permutations
V. E. Tarakanov, V. P. Chistyakov
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.
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Mathematics of the USSR-Sbornik, 1975, 25:4, 559–565
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
\by V.~E.~Tarakanov, V.~P.~Chistyakov
\paper On~the cycle structure of random permutations
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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This publication is cited in the following articles:
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
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
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
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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