Product-free sets in the free semigroup

Published 12 Dec 2018 in math.CO | (1812.04749v1)

Abstract: 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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