Product-free sets in the free semigroup.

Imre Leader,Shoham Letzter,Bhargav Peruvemba Narayanan,Mark Walters

European Journal of Combinatorics（2020）

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摘要

In this paper, we study product-free subsets of the free semigroup over a finite alphabet A. We prove that the maximum density of a product-free subset of the free semigroup over A, with respect to the natural measure that assigns a weight of |A|−n to each word of length n, is precisely 1∕2.

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