Følner sequences and sum‐free sets. (1st December 2014)

• Record Type: Journal Article
• Authors: Eberhard, Sean
• Is Part Of: Bulletin of the London Mathematical Society. Volume 47:Part 1(2015:Feb.)
• Page Start: 21
• Page End: 28
• Publication Date: 2014-12-01
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/blms/bdu091
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract : Erdős showed that every set ofn positive integers contains a subset of size at leastn / ( k + 1 ) containing no solutions tox 1 + ⋯ + x k = y . We prove that the constant1 / ( k + 1 ) here is best possible by showing that if( F m ) is a multiplicative Følner sequence inN, thenF m has nok ‐sum‐free subset of size greater than( 1 / ( k + 1 ) + o ( 1 ) ) | F m | .