University of Cambridge > Talks.cam > Combinatorics Seminar > The number of maximal sum-free subsets of integers

The number of maximal sum-free subsets of integers

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  • UserAndrew Treglown (University of Birmingham)
  • ClockThursday 27 November 2014, 14:30-15:30
  • HouseMR12.

If you have a question about this talk, please contact Andrew Thomason.

A set S of integers is sum-free if x+y is not in S for every x,y in S. Green and independently Sapozhenko proved that there are O(2) sum-free sets in {1,...,n}, thereby resolving a conjecture of Cameron and Erdős.

Cameron and Erdős also 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 talk 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, Sós and Temkin on the structure of sum-free sets. This is joint work with József Balogh, Hong Liu and Maryam Sharifzadeh.

This talk is part of the Combinatorics Seminar series.

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