The number of maximal sum-free subsets of integers

Abstract

Cameron and Erdős raised the question of how many maximal sum-free sets there are in $\{1,\dots ,n\}$, giving a lower bound of $2^{\lfloor n/4\rfloor }$. In this paper we prove that there are in fact at most $2^{(1/4+o(1))n}$ maximal sum-free sets in $\{1,\dots ,n\}$. Our proof makes use of container and removal lemmas of Green as well as a result of Deshouillers, Freiman, Sós and Temkin on the structure of sum-free sets.

10 pages, to appear in the Proceedings of the American Mathematical Society

References in corpus (1)

• The number of the maximal triangle-free graphs

Cited by in corpus (1)

• The number of the maximal triangle-free graphs