Cameron–Erdős conjecture

In combinatorial mathematics, the Cameron–Erdős conjecture is the statement that the number of sum-free sets contained in $\{1,ldots,N\}$ is $Oleft(\{2^\{N/2\; ight)$.

The conjecture was stated by Peter Cameron and Paul Erdős in 1988. [P.J. Cameron and P. Erdős, "On the number of sets of integers with various properties", Number theory (Banff, 1988), de Gruyter, Berlin 1990, pp.61-79] It was proved by Ben Green in 2003. [B. Green, [http://www.arxiv.org/pdf/math.NT/0304058 The Cameron-Erdős conjecture] , 2003.] [B. Green, "The Cameron-Erdős conjecture", Bulletin of the London Mathematical Society 36 (2004) pp.769-778]

A different proof has recently been found by Sasha Sapozhenko. [A. Sapozhenko, "The Cameron-Erdős conjecture", DiscreteMathematics, in press]

ee also

* Erdős conjecture

References