Geodesic
On the number of sum-free sets in an interval of natural numbers
Diskretnaya Matematika, Tome 14 (2002) no. 3, pp. 3-7 
K. G. Omel'yanov; A. A. Sapozhenko. On the number of sum-free sets in an interval of natural numbers. Diskretnaya Matematika, Tome 14 (2002) no. 3, pp. 3-7. http://geodesic.mathdoc.fr/item/DM_2002_14_3_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Cameron P., Erdős P., “On the number of integers with various properties”, Number theory, Proc. 1st Conf. Can. Number Theory Assoc. Banff/Alberta (Mollin R. A., Ed.) 1988, De Gruyter, Berlin, 1990, 61–79

[2] Calkin N. J., “On the number of sum-free sets”, Bull. London Math. Soc., 22 (1990), 141–144 | DOI | MR | Zbl

[3] Mann H. B., Addition theorems: the addition theorems of group theory and number theory, Interscience, New York, 1965 | MR | Zbl

[4] Sapozhenko A. A., “O chisle nezavisimykh mnozhestv v rasshiritelyakh”, Diskretnaya matematika, 13:1 (2001), 56–62 | MR | Zbl