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

This article is cited in 14 scientific papers (total in 14 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 $S_n(\Lambda)$.

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
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

Citation in format AMSBIB
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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:
    1. A. L. Yakymiv, “On permutations with cycle lengths from a random set”, Discrete Math. Appl., 10:6 (2000), 543–551  mathnet  crossref  mathscinet  zmath
    2. 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  mathnet  crossref  crossref  mathscinet  zmath  elib
    3. A. L. Yakymiv, “Limit theorem for the general number of cycles in a random $A$-permutation”, Theory Probab. Appl., 52:1 (2008), 133–146  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. A. L. Yakymiv, “On the Number of $A$-Mappings”, Math. Notes, 86:1 (2009), 132–139  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. A. L. Yakymiv, “A limit theorem for the logarithm of the order of a random $A$-permutation”, Discrete Math. Appl., 20:3 (2010), 247–275  mathnet  crossref  crossref  mathscinet  zmath  elib  elib
    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  mathnet  crossref  crossref  mathscinet  isi
    8. A. L. Yakymiv, “Random $A$-permutations and Brownian motion”, Proc. Steklov Inst. Math., 282 (2013), 298–318  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    9. A. L. Yakymiv, “On the number of cyclic points of random $A$-mapping”, Discrete Math. Appl., 23:5-6 (2013), 503–515  mathnet  crossref  crossref  mathscinet  elib  elib
    10. A. L. Yakymiv, “On a number of components in a random $A$-mapping”, Theory Probab. Appl., 59:1 (2015), 114–127  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    11. A. L. Yakymiv, “On the Number of Components of Fixed Size in a Random $A$-Mapping”, Math. Notes, 97:3 (2015), 468–475  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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  mathnet  crossref  crossref  mathscinet  isi  elib
    13. A. L. Yakymiv, “Asimptotika momentov chisla tsiklov sluchainoi $A$-podstanovki s ostatochnym chlenom”, Diskret. matem., 31:3 (2019), 114–127  mathnet  crossref  mathscinet
    14. A. L. Yakymiv, “Dispersiya chisla tsiklov sluchainoi $A$-podstanovki”, Diskret. matem., 32:3 (2020), 135–146  mathnet  crossref
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