Product-free sets in the free group

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hdl:2117/395672
Document typeConference lecture
Defense date2023
Rights accessOpen Access
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Attribution-NonCommercial-NoDerivs 4.0 International
ProjectCOMBINATORIA GEOMETRICA, ALGEBRAICA Y PROBABILISTICA (AEI-MTM2017-82166-P)
COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONES (AEI-PID2020-113082GB-I00)
COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONES (AEI-PID2020-113082GB-I00)
Abstract
We prove that product-free sets of the free group over a finite alphabet have max-imum density1/2with respect to the natural measure that assigns total weight oneto each set of irreducible words of a given length. This confirms a conjecture ofLeader, Letzter, Narayanan and Walters. In more general terms, we actually provethat stronglyk-product-free sets have maximum density1/kin terms of the saidmeasure. The bounds are tight.
CitationOrtega, M.; Rue, J.; Serra, O. Product-free sets in the free group. A: European Conference on Combinatorics, Graph Theory and Applications. "Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications: EUROCOMB'23. Prague, August 28 - September 1, 2023". 2023, p. 748-753. ISBN 978-80-280-0344-9. DOI 10.5817/CZ.MUNI.EUROCOMB23-103.
ISBN978-80-280-0344-9
Publisher versionhttps://journals.muni.cz/eurocomb/article/view/35637
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