Følner sequences and sum-free sets

Sean Eberhard*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Erdos showed that every set of n positive integers contains a subset of size at least n/(k + 1) containing no solutions to x1 + . . . + xk = y. We prove that the constant 1/(k + 1) here is best possible by showing that if (Fm) is a multiplicative Følner sequence in N, then Fm has no k-sum-free subset of size greater than (1/(k + 1) + o(1))|Fm|.

Original languageEnglish
Pages (from-to)21-28
Number of pages8
JournalBulletin of the London Mathematical Society
Issue number1
Early online date01 Dec 2014
Publication statusPublished - Feb 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014 London Mathematical Society.

ASJC Scopus subject areas

  • General Mathematics


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