The number of maximal sum-free subsets of integers

József Balogh, Hong Liu, Maryam Sharifzadeh, Andrew Treglown

Research output: Contribution to journalArticlepeer-review


Cameron and Erdőos raised the question of how many maximal sum-free sets there are in {1, . . . ,n}, giving a lower bound of 2⌊n/4⌋. In this paper we prove that there are in fact at most 2(1/4+o(1))n maximal sum-free sets in {1, . . . , n}. Our proof makes use of container and removal lemmas of Green as well as a result of Deshouillers, Freiman, Sóos and Temkin on the structure of sum-free sets.

Original languageEnglish (US)
Pages (from-to)4713-4721
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number11
StatePublished - Nov 1 2015

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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