Estimates for the Proportion of Sequences with Small Deviations from the Mean

Kochergin Vadim Vasil'evich

Estimates for the Proportion of Sequences with Small Deviations from the Mean

Kochergin V. V.

Kochergin Vadim Vasil'evich

Head of Chair of Discrete Mathematics, Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

0000-0002-7798-9502

Received: 18 Nov 2025 Accepted: 19 Mar 2026

Published: 2026, vol. 30, issue 1, pp. 126–150

Download full text (In Russian)

Abstract

The problem of the magnitude of the restriction in a $k$-digit set on the permissible deviation from the average count of digits having each of the $k$ values under the condition of a given proportion of such sequences. An approach is proposed that allows monitoring the influence of various parameters on the final result at each stage, and estimates of the accuracy of the approximate solution are provided.

Keywords: $k$-digit hypercube, Stirling's formula, proportion of sequences

BibTeX

@article{IS-Kochergin2026,
  author  = {Kochergin, Vadim Vasil'evich},
  title   = {{Estimates for the Proportion of Sequences with Small Deviations from the Mean}},
  journal = {Intelligent Systems. Theory and Applications},
  year    = {2026},
  volume  = {30},
  number  = {1},
  pages   = {126--150},
}

AMSBIB

\Bibitem{IS-Kochergin2026}
\by V.\,V.~Kochergin
\paper Estimates for the Proportion of Sequences with Small Deviations from the Mean
\jour Intelligent Systems. Theory and Applications
\yr 2026
\vol 30
\issue 1
\pages 126--150
\lang In Russian

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