Product-free sets in the free semigroup. (January 2020) - Leader, Imre; Letzter, Shoham; Narayanan, Bhargav; Walters, Mark
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 .