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Diskr. Mat., 2003, Volume 15, Issue 4, Pages 7–34 (Mi dm214)  

This article is cited in 8 scientific papers (total in 8 papers)

Structural equivalence of $s$-tuples in random discrete sequences

V. G. Mikhailov, A. M. Shoitov


Abstract: Recently there appeared a significant number of papers investigating structural properties of random discrete sequences. They provide a large group of results on structurally equivalent intervals in such sequences. The goal of the present paper is to give a survey of the problems and the known results in this interesting area of discrete probability theory.
This research was supported by the Russian Foundation for Basic Research, grant 02–01–00266, by the grant 1758.2003.1 of the State support of the leading scientific schools of the Russian Federation, and by the grant 2831.2003.09 of the State support of young Russian scientists.

DOI: https://doi.org/10.4213/dm214

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English version:
Discrete Mathematics and Applications, 2003, 13:6, 541–568

Bibliographic databases:

UDC: 519.2
Received: 15.09.2003

Citation: V. G. Mikhailov, A. M. Shoitov, “Structural equivalence of $s$-tuples in random discrete sequences”, Diskr. Mat., 15:4 (2003), 7–34; Discrete Math. Appl., 13:6 (2003), 541–568

Citation in format AMSBIB
\Bibitem{MikSho03}
\by V.~G.~Mikhailov, A.~M.~Shoitov
\paper Structural equivalence of $s$-tuples in random discrete sequences
\jour Diskr. Mat.
\yr 2003
\vol 15
\issue 4
\pages 7--34
\mathnet{http://mi.mathnet.ru/dm214}
\crossref{https://doi.org/10.4213/dm214}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2050747}
\zmath{https://zbmath.org/?q=an:1046.60052}
\transl
\jour Discrete Math. Appl.
\yr 2003
\vol 13
\issue 6
\pages 541--568
\crossref{https://doi.org/10.1515/156939203322733273}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Shoitov, “The Poisson approximation for the number of matches of values of a discrete function from chains”, Discrete Math. Appl., 15:3 (2005), 241–254  mathnet  crossref  crossref  mathscinet  zmath  elib
    2. A. M. Shoitov, “The compound Poisson distribution of the number of matches of values of a discrete function of $s$-tuples in segments of a sequence of random variables”, Discrete Math. Appl., 17:3 (2007), 209–230  mathnet  crossref  crossref  mathscinet  zmath  elib
    3. V. G. Mikhailov, “On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a random sequence”, Discrete Math. Appl., 18:6 (2008), 563–568  mathnet  crossref  crossref  mathscinet  zmath  elib
    4. A. M. Shoitov, “Strukturno ekvivalentnye tsepochki v ravnoveroyatnoi polinomialnoi skheme”, Matem. vopr. kriptogr., 3:3 (2012), 129–151  mathnet  crossref
    5. 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
    6. V. G. Mikhailov, A. M. Shoitov, “On repetitions of long tuples in a Markov chain”, Discrete Math. Appl., 25:5 (2015), 295–303  mathnet  crossref  crossref  mathscinet  isi  elib
    7. 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
    8. V. G. Mikhailov, “On the reduction property of the number of $H$-equivalent tuples of states in a discrete Markov chain”, Discrete Math. Appl., 28:2 (2018), 75–82  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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