Counting sumsets and sum-free sets modulo a prime

被引：22

作者：

Green, B ^{[1
]}

Ruzsa, IZ

机构：

[1] Trinity Coll, Cambridge CB2 1TQ, England

[2] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1364 Budapest, Hungary

来源：

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA | 2004年 / 41卷 / 03期

关键词：

sumset; sum-free set; granularization;

D O I：

10.1556/SScMath.41.2004.3.2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p be a prime. A set A of residues modulo p is said to be sum-free if there axe no solutions to a = a' + a" with a, a', a" is an element of A. We show that there axe 2(p/3+o(p)) such sets. We also count the number of distinct sets of the form B + B, where B is a set of residues modulo p. Once again, there are 2(p/3+o(p)) such sets.

引用

页码：285 / 293

页数：9

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