RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Mat. Zametki, 1975, Volume 18, Issue 6, Pages 929–938 (Mi mz7716)  

This article is cited in 2 scientific papers (total in 2 papers)

The cyclic structure of random permutations

V. F. Kolchin, V. P. Chistyakov

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: Let $\alpha_r$ denote the number of cycles of length $r$ in a random permutation, taking its values with equal probability from among the set $S_n$ of all permutations of length $n$. In this paper we study the limiting behavior of linear combinations of random permutations $\alpha_1,…,\alpha_r$ having the form
$$ \zeta_{n,r}=C_{r1}\alpha_1+…+C_{rr}\alpha_r $$
in the case when $n,r\to\infty$. We shall show that the class of limit distributions for $\zeta_{n,r}$ as $n,r\to\infty$ and $r\ln r/n\to0$ coincides with the class of unbounded divisible distributions. For the random variables $\eta_{n,r}=\alpha_1+2\alpha_2+…+r\alpha_r$, equal to the number of elements in the permutation contained in cycles of length not exceeding $r$, we find limit distributions of the form $r\ln r/n\to0$ и $r=\gamma n$, $0<\gamma<1$.

Full text: PDF file (508 kB)

English version:
Mathematical Notes, 1975, 18:6, 1139–1144

Bibliographic databases:

Document Type: Article
UDC: 519.2
Received: 11.11.1975

Citation: V. F. Kolchin, V. P. Chistyakov, “The cyclic structure of random permutations”, Mat. Zametki, 18:6 (1975), 929–938; Math. Notes, 18:6 (1975), 1139–1144

Citation in format AMSBIB
\Bibitem{KolChi75}
\by V.~F.~Kolchin, V.~P.~Chistyakov
\paper The cyclic structure of random permutations
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 6
\pages 929--938
\mathnet{http://mi.mathnet.ru/mz7716}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=402852}
\zmath{https://zbmath.org/?q=an:0344.60015}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 6
\pages 1139--1144
\crossref{https://doi.org/10.1007/BF01099997}


Linking options:
  • http://mi.mathnet.ru/eng/mz7716
  • http://mi.mathnet.ru/eng/mz/v18/i6/p929

    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. Yu. V. Bolotnikov, V. N. Sachkov, V. E. Tarakanov, “On some classes of random variables on cycles of permutations”, Math. USSR-Sb., 36:1 (1980), 87–99  mathnet  crossref  mathscinet  zmath  isi
    2. A. N. Timashev, “On the distribution of the number of cycles of a given length in the class of permutations with known number of cycles”, Discrete Math. Appl., 11:5 (2001), 471–483  mathnet  crossref  mathscinet  zmath
  • Математические заметки Mathematical Notes
    Number of views:
    This page:153
    Full text:46
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018