Sum-free sets in abelian groups

被引：0

作者：

Ben Green

Imre Z. Ruzsa

机构：

[1] University of Bristol University Walk,School of Mathematics

[2] Hungarian Academy of Sciences,Alfréd Rényi Mathematical Institute

来源：

Israel Journal of Mathematics | 2005年 / 147卷

关键词：

Abelian Group; Dual Problem; London Mathematical Society; Finite Abelian Group; Pigeonhole Principle;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

LetA be a subset of an abelian groupG with |G|=n. We say thatA is sum-free if there do not existx, y, z εA withx+y=z. We determine, for anyG, the maximal densityμ(G) of a sum-free subset ofG. This was previously known only for certainG. We prove that the number of sum-free subsets ofG is 2(μ(G)+o(1))n, which is tight up to theo-term. For certain groups, those with a small prime factor of the form 3k+2, we are able to give an asymptotic formula for the number of sum-free subsets ofG. This extends a result of Lev, Luczak and Schoen who found such a formula in the casen even.

引用

页码：157 / 188

页数：31

共 22 条

[1]

Alon N.(1991)Independent sets in regular graphs and sum-free subsets of abelian groups Israel Journal of Mathematics 73 247-256

[2]

Calkin N. J.(1990)On the number of sum-free sets The Bulletin of the London Mathematical Society 22 141-144

[3]

Diananda P. H.(1969)Maximal sum-free sets of elements of finite groups Proceedings of the Japan Academy 45 1-5

[4]

Yap H. P.(2004)The Cameron-Erdős conjecture The Bulletin of the London Mathematical Society 36 769-778

[5]

Green B. J.(2004)Counting sumsets and sum-free sets in modulo p Studia Scientiarum Mathematicarum Hangarica 41 285-293

[6]

Green B. J.(1998)Product-free subsets of groups The American Mathematical Monthly 105 900-906

[7]

Ruzsa I. Z.(1958)Abschätzungen der asymptotische Dichte von Summenmengen Mathematische Zeitschrift 58 459-484

[8]

Kedlaya K. S.(2002)Cameron-Erdős modulo a prime Finite Fields and their Applications 8 108-119

[9]

Kneser M.(2001)Sum-free sets in abelian groups Israel Journal of Mathematics 125 347-367

[10]

Lev V. F.(1974)A generalisation of the theorem of Cauchy and Davenport Journal of the London Mathematical Society 8 460-462

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