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On the number of permutations with a finite set of cycle lengths. (English. Russian original) Zbl 0897.05006
Proc. Steklov Inst. Math. 207, 233-242 (1995); translation from Tr. Mat. Inst. Steklova 207, 256-267 (1994).
Let $$\Lambda$$ be a set of natural numbers, $$S_n (\Lambda)$$ the set of all permutations of degree $$n$$ having only cycles with lengths from the set $$\Lambda$$, and $$| S_n (\Lambda)|$$ the number of elements of the finite set $$S_n (\Lambda)$$. We study the asymptotic behavior of $$| S_n (\Lambda)|$$ as $$n\to\infty$$, depending on the structure of a fixed set $$\Lambda$$. The corresponding problem was first posed in [E. A. Bender, SIAM Rev. 16, 485-515 (1974; Zbl 0294.05002)]. The case $$|\Lambda |= \infty$$ has been investigated in a number of papers by the author. In the present paper we investigate the case $$|\Lambda |<\infty$$.
For the entire collection see [Zbl 0833.00028].
##### MSC:
 05A16 Asymptotic enumeration 05A05 Permutations, words, matrices 20B30 Symmetric groups
##### Keywords:
permutations; asymptotic behavior