descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Conference object 01 Jan 2023Embargo end date: 01 Jan 2023Publisher:Masaryk University PressJournal:Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications

Authors: Ortega Sánchez Colomer, Miquel; Rué Perna, Juan José; Serra Albó, Oriol;

doi: 10.5817/cz.muni.eurocomb23-103 , 10.1112/mtk.12255 , 10.48550/arxiv.2302.03748

arXiv: http://arxiv.org/abs/2302.03748

handle: 2117/424823 , 2117/395672

Product-free sets in the free group

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Abstract

We prove that product-free sets of the free group over a finite alphabet have maximum density $1/2$ with respect to the natural measure that assigns total weight one to each set of irreducible words of a given length. This confirms a conjecture of Leader, Letzter, Narayanan and Walters. In more general terms, we actually prove that strongly $k$-product-free sets have maximum density $1/k$ in terms of the said measure. The bounds are tight.

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
Centre de Recerca Matemàtica
Spain
Institució dels Centres de Recerca de Catalunya
Spain
Universitat Politècnica de Catalunya
Spain

Keywords

Combinatorial analysis, conjunts lliures de sumes, Classificació AMS::05 Combinatorics::05D Extremal combinatorics, combinatoria aditiva, Combinatoria, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups, 510, 004, Free groups, Classificació AMS::20 Group theory and generalizations, Combinatoria aditiva, Combinacions (Matemàtica), Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria, FOS: Mathematics, Classificació AMS::20 Group theory and generalizations::20M Semigroups, Mathematics - Combinatorics, Semigrups, Combinatorics (math.CO), Semigroups, Grups lliures, grup lliure

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