Product-free sets in the free semigroup
Copyright policy )Product-free sets in the free semigroup
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
- Rutgers, The State University of New Jersey United States
- University of London United Kingdom
- Queen Mary University of London United Kingdom
- ETH Institute for Theoretical Studies Switzerland
- University of Cambridge United Kingdom
Additive bases, including sumsets, Free semigroups, generators and relations, word problems, FOS: Mathematics, Mathematics - Combinatorics, 20M05 (Primary), 05D05 (Secondary), Combinatorics (math.CO), General structure theory for semigroups
Additive bases, including sumsets, Free semigroups, generators and relations, word problems, FOS: Mathematics, Mathematics - Combinatorics, 20M05 (Primary), 05D05 (Secondary), Combinatorics (math.CO), General structure theory for semigroups
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