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K. G. Omelyanov, A. A. Sapozhenko

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

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)|.

We prove that

s (t, n) = O(2 ^n/2)

for t ≥ n ^3/4log n, where log t = log₂ t.

Discrete Mathematics and Applications, Walter de Gruyter

Print ISSN: 0924-9266
Volume: 13, 12/2003
Pages: 637 - 643

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