Product-free sets in the free semigroup

被引:2
作者
Leader, Imre [1 ]
Letzter, Shoham [2 ]
Narayanan, Bhargav [3 ]
Walters, Mark [4 ]
机构
[1] Univ Cambridge, Dept Pure Math & Math Stat, Wilberforce Rd, Cambridge CB3 0WB, England
[2] ETH, Inst Theoret Studies, CH-8092 Zurich, Switzerland
[3] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA
[4] Queen Mary Univ London, Sch Math Sci, London E1 4NS, England
关键词
SUM-FREE SETS; FREE SUBSETS;
D O I
10.1016/j.ejc.2019.103003
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we study product-free subsets of the free semigroup over a finite alphabet A. We prove that the maximum density of a product-free subset of the free semigroup over A, with respect to the natural measure that assigns a weight of vertical bar A vertical bar(-n) to each word of length n, is precisely 1/2. (C) 2019 Elsevier Ltd. All rights reserved.
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页数:6
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