Product-free sets in the free group
Combinatorics
2024-09-12 v2
Abstract
We prove that product-free sets of the free group over a finite alphabet have maximum density with respect to the natural measure that assigns total weight one to each set of irreducible words of a given size. This confirms a conjecture of Leader, Letzter, Narayanan and Walters. In more general terms, we actually prove that strongly -product-free sets have maximum density in terms of the said measure.
Keywords
Cite
@article{arxiv.2302.03748,
title = {Product-free sets in the free group},
author = {Miquel Ortega and Juanjo Rué and Oriol Serra},
journal= {arXiv preprint arXiv:2302.03748},
year = {2024}
}
Comments
10 pages. Uploaded accepted version including some changes suggested by anonymous referees