Sets of integers with no large sum-free subset

2013/01/31 by Sean Eberhard, Ben Green, Freddie Manners
Engineering · Mathematics · #Advanced Topology and Set Theory #Limits and Structures in Graph Theory #graph theory and CDMA systems #math.CO #math.NT

paper · pdf · doi:10.4007/annals.2014.180.2.5

Ann. Math 180 (2014), no. 2, 621--652. Arxiv v3 corrects a very small inaccuracy in Lemma 6.3

arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

Answering a question of P. Erdos from 1965, we show that for every eps>0 there is a set A of n integers with the following property: every subset A' of A with at least (1/3 + eps)n elements contains three distinct elements x,y,z with x + y = z.

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