On the structure of sum-free sets, 2

Jean Marc Deshouillers*, Gregory A. Freiman, Vera Sós, Mikhail Temkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


A finite set of positive integers is called sum-free if double-struck A∩n (double-struck A + double-struck A) is empty, where double-struck A + double-struck A denotes the set of sums of pairs of non necessarily distinct elements from double-struck A. Improving upon a previous result by G.A. Freiman, a precise description of the structure of sum-free sets included in [1, M] with cardinality larger than 0.4M - x for M ≥ M0(x) (where x is an arbitrary given number) is given.

Original languageAmerican English
Pages (from-to)149-161
Number of pages13
StatePublished - 1999
Externally publishedYes


  • Additive number theory
  • Arithmetic progressions
  • Combinatorial number theory
  • Sum-free sets


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