A note on the density of sum-free sets
type: Item
instance of: scholarly article
title: A note on the density of sum-free sets
zbMATH Open document ID: 0819.05008
DOI: 10.1016/0097-3165(95)90098-5
author: Tomasz Łuczak
published in: Journal of Combinatorial Theory. Series A
publication date: 1995-08-27T00:00:00Z
review text: Obviously, each set \(A\) of upper density larger than \({1\over 2}\) contains two different elements \(x,y\) such that \(x+ y\in A\) (it is enough to take any \(x\in A\) and \(y\in A\cap(A- x)\)). On the other hand, the set of all odd numbers is sum-free and has density \({1\over 2}\). In this note we shall prove that this set is, in a way, the unique extremal set for this property, i.e., the ``threshold density'' of the property that set \(A\) is sum-free drops down to \({2\over 5}\) under the assumption that \(A\) contains at least one even number.
Mathematics Subject Classification ID: 05A99
Mathematics Subject Classification ID: 11B75
zbMATH DE Number: 753623
zbMATH Keywords: sum-free sets
zbMATH Keywords: density
zbMATH Keywords: extremal set
MaRDI profile type: Publication
full work available at URL: 0097-3165(95)90098-5
OpenAlex ID: W2030415839
description: scientific article; zbMATH DE number 753623