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Matematicheskie Zametki, 1997, Volume 62, Issue 6, Pages 881–891
DOI: https://doi.org/10.4213/mzm1677
(Mi mzm1677)
 

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
References:
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
English version:
Mathematical Notes, 1997, Volume 62, Issue 6, Pages 739–746
DOI: https://doi.org/10.1007/BF02355462
Bibliographic databases:
UDC: 511.33+519.115
Language: Russian
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
Citation in format AMSBIB
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\paper On two classes of permutations with number-theoretic conditions on the lengths of the cycles
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\pages 881--891
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\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 6
\pages 739--746
\crossref{https://doi.org/10.1007/BF02355462}
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  • https://doi.org/10.4213/mzm1677
  • https://www.mathnet.ru/eng/mzm/v62/i6/p881
  • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические заметки Mathematical Notes
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