The Cameron–Erdős conjecture

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• 作者：Alex ; er A. Sapozhenko
• 关键词：Independent set ; Sum-free set ; Container method ; Cameron– ; Erdő ; s conjecture
• 刊名：Discrete Mathematics
• 出版年：2008
• 期刊代码：47_0012365x
• 类别：cp
• 出版时间：6 October 2008
• 卷：308
• 期：19
• 页码：4361-4369
• 文件大小：179 K

摘要

A subset A of integers is said to be sum-free if a+bA for any a,bA. Let s(n) be the number of sum-free sets in interval [1,n] of integers. P. Cameron and P. Erdős conjectured that s(n)=O(2^n/2). We show that for even n and for odd n, where are absolute constants, thereby proving the conjecture.