Year: 2014
Type: article
Abstract: Erdős showed that every set of n positive integers contains a subset of size at least n / ( k + 1 ) containing no solutions to x 1 + ⋯ + x k = y . We prove that the constant 1 / ( k + 1 ) here is best possible by showing that if ( F m ) is a multiplicative Følner sequence in N, then F m has no k-sum-free subset of size greater than ( 1 / ( k + 1 ) + o ( 1 ) ) | F m | .
DOI: 10.1112/blms/bdu091
Author: Sean Eberhard
Institution: University of Oxford
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2051545604