Product-free sets in the free semigroup

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 $1/2$.

8 pages, submitted