THE NUMBER OF MAXIMAL SUM-FREE SUBSETS OF INTEGERS

被引：17

作者：

Balogh, Jozsef ^{[1
,2
]}

Liu, Hong ^{[1
]}

Sharifzadeh, Maryam ^{[1
]}

Treglown, Andrew ^{[3
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary

[3] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 143卷 / 11期

关键词：

LEMMA;

D O I：

10.1090/S0002-9939-2015-12615-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：4713 / 4721

页数：9

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