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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
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
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
Linking options:
https://www.mathnet.ru/eng/dm223https://doi.org/10.4213/dm223 https://www.mathnet.ru/eng/dm/v15/i4/p141
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