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

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Diskretnaya Matematika, 2003, Volume 15, Issue 4, Pages 7–34
DOI: https://doi.org/10.4213/dm214 (Mi dm214)

This article is cited in 12 scientific papers (total in 12 papers)

Structural equivalence of

s

$s$ -tuples in random discrete sequences

V. G. Mikhailov, A. M. Shoitov

Full-text PDF (2496 kB) Citations (12)

References:

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

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.

Received: 15.09.2003

English version:
Discrete Mathematics and Applications, 2003, Volume 13, Issue 6, Pages 541–568
DOI: https://doi.org/10.1515/156939203322733273

Bibliographic databases:

Document Type: Article

UDC: 519.2

Language: Russian

Citation: V. G. Mikhailov, A. M. Shoitov, “Structural equivalence of

s

$s$ -tuples in random discrete sequences”, Diskr. Mat., 15:4 (2003), 7–34; Discrete Math. Appl., 13:6 (2003), 541–568

Citation in format AMSBIB

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\jour Discrete Math. Appl.

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Linking options:

https://www.mathnet.ru/eng/dm214

https://doi.org/10.4213/dm214

https://www.mathnet.ru/eng/dm/v15/i4/p7

This publication is cited in the following 12 articles:

V. I. Kruglov, “Tochnaya formula dlya matematicheskogo ozhidaniya chisla par odinakovykh $s$ -tsepochek v sluchainoi dvoichnoi posledovatelnosti s zadannym kolichestvom nulei i edinits”, PDM. Prilozhenie, 2024, no. 17, 9–11
V. G. Mikhailov, A. M. Shoitov, A. V. Volgin, “On Series of $H$ -Equivalent Tuples in Markov Chains”, Proc. Steklov Inst. Math., 316 (2022), 254–267
V. A. Kopyttsev, V. G. Mikhailov, “Method of Moments and Sums of Random Indicators”, Proc. Steklov Inst. Math., 316 (2022), 220–232
V. G. Mikhailov, N. M. Mezhennaya, “Normal approximation for $U$ - and $V$ -statistics of a stationary absolutely regular sequence”, Sib. elektron. matem. izv., 17 (2020), 672–682
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
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
V. G. Mikhailov, A. M. Shoitov, “On repetitions of long tuples in a Markov chain”, Discrete Math. Appl., 25:5 (2015), 295–303
V. G. Mikhailov, A. M. Shoitov, “O chislakh mnozhestv ekvivalentnykh tsepochek v posledovatelnosti nezavisimykh sluchainykh velichin”, Matem. vopr. kriptogr., 4:1 (2013), 77–86
A. M. Shoitov, “Strukturno ekvivalentnye tsepochki v ravnoveroyatnoi polinomialnoi skheme”, Matem. vopr. kriptogr., 3:3 (2012), 129–151
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
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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