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Diskretnaya Matematika, 2003, Volume 15, Issue 4, Pages 141–147
DOI: https://doi.org/10.4213/dm223
(Mi dm223)
 

This article is cited in 5 scientific papers (total in 5 papers)

On the number and structure of sum-free sets in a segment of positive integers

K. G. Omel'yanov, A. A. Sapozhenko
Full-text PDF (527 kB) Citations (5)
References:
Abstract: A set $A$ of integers is called sum-free if $a+b\notin A$ for any $a,b\in A$. For any real numbers $q\le p$ we denote by $[q,p]$ the set of real numbers $x$ such that $q\le x\le p$. Let $S(t,n)$ stand for the family of all sum-free subsets $A\subseteq[t,n]$, and $s(t,n)=|S(t,n)|$.
We prove that
\begin{equation*} s(t,n)=O(2^{n/2}) \end{equation*}
for $t\ge n^{3/4}\log n$, where $\log t=\log_2t$.
This research was supported by the Russian Foundation for Basic Research, grant 01–01–00266.
Received: 09.09.2003
English version:
Discrete Mathematics and Applications, 2003, Volume 13, Issue 6, Pages 637–643
DOI: https://doi.org/10.1515/156939203322733345
Bibliographic databases:
UDC: 519.6
Language: Russian
Citation: K. G. Omel'yanov, A. A. Sapozhenko, “On the number and structure of sum-free sets in a segment of positive integers”, Diskr. Mat., 15:4 (2003), 141–147; Discrete Math. Appl., 13:6 (2003), 637–643
Citation in format AMSBIB
\Bibitem{OmeSap03}
\by K.~G.~Omel'yanov, A.~A.~Sapozhenko
\paper On the number and structure of sum-free sets in a segment of positive integers
\jour Diskr. Mat.
\yr 2003
\vol 15
\issue 4
\pages 141--147
\mathnet{http://mi.mathnet.ru/dm223}
\crossref{https://doi.org/10.4213/dm223}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2050996}
\zmath{https://zbmath.org/?q=an:1054.11014}
\transl
\jour Discrete Math. Appl.
\yr 2003
\vol 13
\issue 6
\pages 637--643
\crossref{https://doi.org/10.1515/156939203322733345}
Linking options:
  • https://www.mathnet.ru/eng/dm223
  • https://doi.org/10.4213/dm223
  • https://www.mathnet.ru/eng/dm/v15/i4/p141
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Дискретная математика
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