Product-free sets in the free semigroup

Imre Leader, Shoham Letzter, Bhargav Narayanan, Mark Walters

Research output: Contribution to journalArticle


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.

Original languageEnglish (US)
Article number103003
JournalEuropean Journal of Combinatorics
StatePublished - Jan 2020

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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