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

Abstract

A set A of integers is called sum-free if a + b ∉ A for any a, b ∈ A. For any real numbers q ≤ p we denote by [q, p] the set of real numbers x such that q ≤ x ≤ p. Let S (t, n) stand for the family of all sum-free subsets A ⊆ [t, n], and s (t, n) = |S (t, n)|.