This article is cited in 6 papers

On the number of sum-free sets in an interval of natural numbers

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 an arbitrary $\varepsilon>0$, let $s_{\varepsilon}(n)$ denote the number of sum-free sets in the segment $[(1/4+\varepsilon)n,n]$. We prove that for any $\varepsilon>0$ there exists a constant $c =c(\varepsilon)$ such that
$$ s_{\varepsilon}(n)\le c2^{n/2}. $$

This research was supported by the Russian Foundation for Basic Research, grant 01–01–00266.

UDC: 511.2

Received: 10.04.2002

DOI: 10.4213/dm248

 English version: Discrete Mathematics and Applications, 2002, 12:4, 319–323

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