On the number of sum-free sets in a segment of positive integers

Abstract

Abstract A set A of integers is called sum-free if a + b ∉ A for any a, b ∈ A. For an arbitrary Ɛ > 0, let sƐ(n) denote the number of sum-free sets in the segment [(1/4 + Ɛ)n, n]. We prove that for any Ɛ > 0 there exists a constant c = c(Ɛ) such that sƐ(n) ≤ c2n/2. This research was supported by the Russian Foundation for Basic Research, grant 01-01-00266.