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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 4, Pages 818–828 (Mi tvp260)  

This article is cited in 6 scientific papers (total in 6 papers)

Short Communications

Random mappings of finite sets with a known number of components

A. N. Timashev

Academy of Federal Security Service of Russian Federation

Abstract: We consider the class of all one-to-one mappings of an $n$-element set into itself, each of which has exactly $N$ connected components. Letting $n,N\to\infty$, we find that the asymptotic behavior of the mean and variance of the random variable is equal to the number of components of a given size in a mapping that is selected at random and is equiprobable among the elements of the mentioned class, and we prove the Poisson and local normal limit theorems for this random variable. Asymptotic estimates are found for the number of mappings with $N$ components, among which there are exactly $k$ components of a fixed size.

Keywords: random mapping, local limit theorem, asymptotic estimators, components.

DOI: https://doi.org/10.4213/tvp260

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English version:
Theory of Probability and its Applications, 2004, 48:4, 741–751

Bibliographic databases:

Received: 21.11.2000

Citation: A. N. Timashev, “Random mappings of finite sets with a known number of components”, Teor. Veroyatnost. i Primenen., 48:4 (2003), 818–828; Theory Probab. Appl., 48:4 (2004), 741–751

Citation in format AMSBIB
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\pages 741--751
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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. N. Timashov, “Limit theorems for the joint distribution of component sizes of a random mapping with a known number of components”, Discrete Math. Appl., 21:1 (2011), 39–46  mathnet  crossref  crossref  mathscinet  elib
    2. A. N. Timashov, “Asymptotic expansions for the distribution of the number of components in random mappings and partitions”, Discrete Math. Appl., 21:3 (2011), 291–301  mathnet  crossref  crossref  mathscinet  elib
    3. 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
    4. 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
    5. 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
    6. 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
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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