Product-free sets in the free group
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916388096966656 |
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| author | Ortega, Miquel Rué, Juanjo Serra, Oriol |
| author_facet | Ortega, Miquel Rué, Juanjo Serra, Oriol |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_03748 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Product-free sets in the free group Ortega, Miquel Rué, Juanjo Serra, Oriol Combinatorics 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. |
| title | Product-free sets in the free group |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2302.03748 |