TY - JOUR

T1 - The number of maximal sum-free subsets of integers

AU - Balogh, József

AU - Liu, Hong

AU - Sharifzadeh, Maryam

AU - Treglown, Andrew

N1 - Publisher Copyright:
© 2015 American Mathematical Society.

PY - 2015/11/1

Y1 - 2015/11/1

N2 - 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.

AB - 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.

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U2 - 10.1090/S0002-9939-2015-12615-9

DO - 10.1090/S0002-9939-2015-12615-9

M3 - Article

AN - SCOPUS:84940434908

VL - 143

SP - 4713

EP - 4721

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11

ER -