Article collection "Mathematical Problems of Cybernetics" ¹12, Moscow, 2003

Authors:Sapozhenko A.A.

A proof of the Cameron–Erdős conjecture on the number of sum-free sets

Abstract:

A subset 𝐴 of integers is said to be sum-free if for any 𝑎, 𝑏 ∈ 𝐴 the number 𝑎+𝑏 does not belong to the set 𝐴. Let (𝑡, 𝑛) be the number of all subsets of set {𝑡, 𝑡+1, . . . , 𝑛} that are sum-free and 𝑠^{1}(𝑛) be the number of subsets of the odd integers from the closed interval [1, 𝑛]. In the present article we prove that (1, 𝑛) ∼ 𝑠(𝑛/3, 𝑛) + 𝑠^{1}(𝑛). A proof of the Cameron–Erdős conjecture follows as a corollary from this statement.

Keywords:

Cameron–Erdős conjecture, container system, graph theory

Publication language:russian, pages:10 (p. 5-14)

Research direction:

Mathematical problems and theory of numerical methods