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Mat. Vopr. Kriptogr., 2012, Volume 3, Issue 3, Pages 129–151 (Mi mvk64)  

This article is cited in 1 scientific paper (total in 1 paper)

Structurally equivalent tuples in the equiprobable polynomial scheme

A. M. Shoitov

Academy of Cryptography of the Russian Federation, Moscow

Abstract: Let $X_1,…,X_n$ be a sequence of independent random variables with the uniform distribution on the set $\{1,…,N\}$. We describe limit discrete distributions of the number of $k$-element sets consisting of structurally equivalent $s$-tuples for $N,n,s\to\infty$, $sN^{-1}\to\alpha\in(0,1)$, $n(N)_sN^{-s}\to\lambda\in(0,\infty)$ and arbitrary $k\geqslant2$. The proofs are based on the Chen–Stein method.

Key words: sequences of independent trials, equiprobable polynomial scheme, structurally equivalent s-tuples, Chen–Stein method.

DOI: https://doi.org/10.4213/mvk64

Full text: PDF file (186 kB)
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UDC: 519.212.2+519.214.5
Received 20.V.2011

Citation: A. M. Shoitov, “Structurally equivalent tuples in the equiprobable polynomial scheme”, Mat. Vopr. Kriptogr., 3:3 (2012), 129–151

Citation in format AMSBIB
\Bibitem{Sho12}
\by A.~M.~Shoitov
\paper Structurally equivalent tuples in the equiprobable polynomial scheme
\jour Mat. Vopr. Kriptogr.
\yr 2012
\vol 3
\issue 3
\pages 129--151
\mathnet{http://mi.mathnet.ru/mvk64}
\crossref{https://doi.org/10.4213/mvk64}


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    This publication is cited in the following articles:
    1. 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
  • Математические вопросы криптографии
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