The number of maximal sum-free subsets of integers

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  • University of Illinois, Urbana Champaign
  • Univ Illinois


Cameron and Erdos 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, Sos and Temkin on the structure of sum-free sets.


Original languageEnglish
Pages (from-to)4713-4722
Number of pages10
JournalProceedings of the American Mathematical Society
Issue number11
Early online date2 Apr 2015
Publication statusPublished - Nov 2015