Product-free sets in the free group

EUROCOMB’23

Miquel Ortega Juanjo Rué Oriol Serra

https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-103

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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.

Pages:
748–753
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https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-103

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Copyright © 2023 Miquel Ortega, Juanjo Rué, Oriol Serra

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