Product-free sets in the free semigroup. (January 2020)

• Record Type: Journal Article
• Authors: Leader, Imre; Letzter, Shoham; Narayanan, Bhargav; Walters, Mark
• Is Part Of: European journal of combinatorics. Volume 83(2020)
• Publication Date: 2020-01
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2019.103003
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: 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 | A | − n to each word of length n, is precisely 1 ∕ 2 .