The number of maximal sum-free subsets of integers

Abstract: Cameron and Erd\H{o}s 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, S\'os and Temkin on the structure of sum-free sets.