The number of maximal sum-free subsets of integers

Jozsef Balogh; Hong Liu; Maryam Sharifzadeh; Andrew Treglown

doi:10.1090/S0002-9939-2015-12615-9

The number of maximal sum-free subsets of integers

Jozsef Balogh
, Hong Liu
, Maryam Sharifzadeh
, Andrew Treglown

Mathematics

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

299 Downloads (Pure)

Abstract

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 language	English
Pages (from-to)	4713-4722
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	11
Early online date	2 Apr 2015
DOIs	https://doi.org/10.1090/S0002-9939-2015-12615-9
Publication status	Published - Nov 2015

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10.1090/S0002-9939-2015-12615-9

Balogh_et_al_Number_Maximal_Sun-Free_Subsets_Proceedings_American_Mathematical_Society_2015_Post-Print
First published in Proceedings of the American Mathematical Society in 2015, published by the American Mathematical Society. Final published version available online at: http://dx.doi.org/10.1090/S0002-9939-2015-12615-9 Checked July 2015
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Cite this

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AU - Liu, Hong

AU - Sharifzadeh, Maryam

AU - Treglown, Andrew

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N2 - 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.

AB - 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.

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The number of maximal sum-free subsets of integers

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