Diskretnaya Matematika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Diskr. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Diskr. Mat., 2000, Volume 12, Issue 4, Pages 53–62 (Mi dm357)  

This article is cited in 4 scientific papers (total in 4 papers)

On permutations with cycle lengths from a random set

A. L. Yakymiv


Abstract: Let $\xi_1,…,\xi_n,…$ be a sequence of independent Bernoulli random variables which take the value 1 with probability $\sigma\in (0,1]$. Given this sequence, we construct the random set $A\subseteq\mathbf N=\{1,2,3,…\}$ as follows: a number $n\in\mathbf N$ is included in $A$ if and only if $\xi_n=1$. Let $T_n=T_n(A)$ denote the set of the permutations of degree $n$ whose cycle lengths belong to the set $A$. In this paper, we find the asymptotic behaviour of the number of elements of the set $T_n(A)$ as $n\to\infty$.
For any fixed $A$, the uniform distribution is defined on $T_n(A)$. Under these hypotheses, limit theorems are obtained for the total number of cycles and the number of cycles of a fixed length in a random permutation in $T_n(A)$.
Similar problems were earlier solved for various classes of deterministic sets $A$.
This research was supported by the Russian Foundation for Basic Research, grants 00–15–96136 and 00–01–00090.

DOI: https://doi.org/10.4213/dm357

Full text: PDF file (654 kB)
References: PDF file   HTML file

English version:
Discrete Mathematics and Applications, 2000, 10:6, 543–551

Bibliographic databases:

UDC: 519.2
Received: 25.04.2000

Citation: A. L. Yakymiv, “On permutations with cycle lengths from a random set”, Diskr. Mat., 12:4 (2000), 53–62; Discrete Math. Appl., 10:6 (2000), 543–551

Citation in format AMSBIB
\Bibitem{Yak00}
\by A.~L.~Yakymiv
\paper On permutations with cycle lengths from a random set
\jour Diskr. Mat.
\yr 2000
\vol 12
\issue 4
\pages 53--62
\mathnet{http://mi.mathnet.ru/dm357}
\crossref{https://doi.org/10.4213/dm357}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1826179}
\zmath{https://zbmath.org/?q=an:1046.60009}
\transl
\jour Discrete Math. Appl.
\yr 2000
\vol 10
\issue 6
\pages 543--551


Linking options:
  • http://mi.mathnet.ru/eng/dm357
  • https://doi.org/10.4213/dm357
  • http://mi.mathnet.ru/eng/dm/v12/i4/p53

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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 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
    2. 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
    3. Lugo, M, “Profiles of permutaions”, Electronic Journal of Combinatorics, 16:1 (2009), R99  mathscinet  zmath  isi
    4. 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
  • Дискретная математика
    Number of views:
    This page:291
    Full text:151
    References:35
    First page:1

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021