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Diskr. Mat., 2008, Volume 20, Issue 4, Pages 113–119 (Mi dm1031)  

This article is cited in 3 scientific papers (total in 3 papers)

On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a random sequence

V. G. Mikhailov


Abstract: In a long enough sequence of discrete random variables, as a rule, an $s$-tuple exists of nontrivial structure, that is, a tuple with at least one repeated symbol. We consider the case where the sequence consists of $n+s-1$ independent random variables taking the values $1,…,N$ with equal probabilities. It is shown that as $n\to\infty$, $ns^3N^{-2}\to0$ the probability of that in the sequence $s$-tuples exist with the same nontrivial structure is equal to $1-(1+n/N)^se^{-sn/N}(1+o(1))$.

DOI: https://doi.org/10.4213/dm1031

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English version:
Discrete Mathematics and Applications, 2008, 18:6, 563–568

Bibliographic databases:

UDC: 519.2
Received: 28.11.2006
Revised: 15.09.2008

Citation: V. G. Mikhailov, “On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a random sequence”, Diskr. Mat., 20:4 (2008), 113–119; Discrete Math. Appl., 18:6 (2008), 563–568

Citation in format AMSBIB
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\by V.~G.~Mikhailov
\paper On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a~random sequence
\jour Diskr. Mat.
\yr 2008
\vol 20
\issue 4
\pages 113--119
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\crossref{https://doi.org/10.4213/dm1031}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2500609}
\zmath{https://zbmath.org/?q=an:1175.60052}
\elib{http://elibrary.ru/item.asp?id=20730271}
\transl
\jour Discrete Math. Appl.
\yr 2008
\vol 18
\issue 6
\pages 563--568
\crossref{https://doi.org/10.1515/DMA.2008.042}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-57349186026}


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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. M. Shoitov, “Strukturno ekvivalentnye tsepochki v ravnoveroyatnoi polinomialnoi skheme”, Matem. vopr. kriptogr., 3:3 (2012), 129–151  mathnet  crossref
    2. V. G. Mikhailov, A. M. Shoitov, “O chislakh mnozhestv ekvivalentnykh tsepochek v posledovatelnosti nezavisimykh sluchainykh velichin”, Matem. vopr. kriptogr., 4:1 (2013), 77–86  mathnet  crossref
    3. V. G. Mikhailov, “On the probability of existence of substrings with the same structure in a random sequence”, Discrete Math. Appl., 27:6 (2017), 377–386  mathnet  crossref  crossref  mathscinet  isi  elib
  • Дискретная математика
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