Product-free sets in the free group
| Autor: | Ortega, Miquel, Rué, Juanjo, Serra, Oriol |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Mathematika, Volume70, Issue3, July 2024 Paper e12255 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/mtk.12255 |
| Popis: | 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 size. 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. Comment: 10 pages. Uploaded accepted version including some changes suggested by anonymous referees |
| Databáze: | arXiv |
| Externí odkaz: |
|