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

Title:
On the number of sum-free sets in a segment of positive integers
Authors:
A. A. Sapozhenko, K G Omel'yanov
Source:
Discrete Mathematics and Applications. 12:319-324
Publisher Information:
Walter de Gruyter GmbH, 2002.
Publication Year:
2002
Subject Terms:
Other combinatorial number theory, 0101 mathematics, 01 natural sciences
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1569-3929
0924-9265
DOI:
10.1515/dma-2002-0402
Access URL:
https://zbmath.org/2095511
https://www.degruyter.com/view/j/dma.2002.12.issue-4/dma-2002-0402/dma-2002-0402.xml
Accession Number:
edsair.doi.dedup.....1c26ec646619680a706a8c91e48abb68
Database:
OpenAIRE

Further Information

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.