2020/09/14 by Yasuaki Gyoda, Gyoda, Yasuaki
Computer Science · #11B57 #11E99 #13F60 #Computability, Logic, AI Algorithms #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2009.06473
openalex publication_date 2020/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We find a duality between two well-known trees, the Calkin-Wilf tree and the Stern-Brocot tree, derived from cluster algebra theory. The vertex sets of these trees are the set of rational numbers, and they have cluster structures induced by one-punctured torus. In particular, the Calkin-Wilf tree is an example of the structure given by initial-seed mutations.