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 Mat. Zametki, 1997, Volume 62, Issue 6, Pages 881–891 (Mi mz1677)

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 $S_n(\Lambda)$.

DOI: https://doi.org/10.4213/mzm1677

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English version:
Mathematical Notes, 1997, 62:6, 739–746

Bibliographic databases:

UDC: 511.33+519.115

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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• http://mi.mathnet.ru/eng/mz1677
• https://doi.org/10.4213/mzm1677
• http://mi.mathnet.ru/eng/mz/v62/i6/p881

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
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5. A. L. Yakymiv, “Limit Theorem for the Middle Members of Ordered Cycle Lengths in Random $A$-Permutations”, Theory Probab. Appl., 54:1 (2010), 114–128
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7. A. L. Yakymiv, “Asymptotics of the Moments of the Number of Cycles of a Random $A$-Permutation”, Math. Notes, 88:5 (2010), 759–766
8. A. L. Yakymiv, “Random $A$-permutations and Brownian motion”, Proc. Steklov Inst. Math., 282 (2013), 298–318
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10. A. L. Yakymiv, “On a number of components in a random $A$-mapping”, Theory Probab. Appl., 59:1 (2015), 114–127
11. A. L. Yakymiv, “On the Number of Components of Fixed Size in a Random $A$-Mapping”, Math. Notes, 97:3 (2015), 468–475
12. A. L. Yakymiv, “Limit theorems for the logarithm of the order of a random $A$-mapping”, Discrete Math. Appl., 27:5 (2017), 325–338
13. A. L. Yakymiv, “Asimptotika momentov chisla tsiklov sluchainoi $A$-podstanovki s ostatochnym chlenom”, Diskret. matem., 31:3 (2019), 114–127
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