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
SN - 0002-9939
VL - 143
SP - 4713
EP - 4721
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 11
ER -