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Product-free sets in the free semigroup

Leader, I; Letzter, S; Narayanan, B; Walters, M; (2020) Product-free sets in the free semigroup. European Journal of Combinatorics , 83 , Article 103003. 10.1016/j.ejc.2019.103003. Green open access

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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.

Type: Article
Title: Product-free sets in the free semigroup
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.ejc.2019.103003
Publisher version: https://doi.org/10.1016/j.ejc.2019.103003
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10107267
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