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This article is cited in 17 scientific papers (total in 17 papers)
On two classes of permutations with number-theoretic conditions on the lengths of the cycles
A. I. Pavlov Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
Let $\Lambda$ be an arbitrary set of positive integers and $S_n(\Lambda)$ the set of all permutations of degree $n$ for which the lengths of all cycles belong to the set $\Lambda$. In the paper the asymptotics of the ratio $|S_n(\Lambda)|/n!$ as $n\to\infty$ is studied in the following cases: 1) $\Lambda$ is the union of finitely many arithmetic progressions, 2) $\Lambda$ consists of all positive integers that are not divisible by any number from a given finite set of pairwise coprime positive integers. Here $|S_n(\Lambda)|$ stands for the number of elements in the finite set $S_n(\Lambda)$.
Received: 12.02.1996
Citation:
A. I. Pavlov, “On two classes of permutations with number-theoretic conditions on the lengths of the cycles”, Mat. Zametki, 62:6 (1997), 881–891; Math. Notes, 62:6 (1997), 739–746
Linking options:
https://www.mathnet.ru/eng/mzm1677https://doi.org/10.4213/mzm1677 https://www.mathnet.ru/eng/mzm/v62/i6/p881
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Abstract page: | 362 | Full-text PDF : | 203 | References: | 44 | First page: | 2 |
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