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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 𝑠1(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) + 𝑠1(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
Russian source text:
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