VOL. 88 | 2023 Cluster duality between Calkin–Wilf tree and Stern–Brocot tree
Yasuaki Gyoda

Editor(s) Yukari Ito, Akira Ishii, Osamu Iyama

Adv. Stud. Pure Math., 2023: 491-516 (2023) DOI: 10.2969/aspm/08810491

Abstract

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 positive rational numbers, and they have cluster structures induced by a one-punctured torus. In particular, the Calkin–Wilf tree is an example of the structure given by initial-seed mutations.

Information

Published: 1 January 2023
First available in Project Euclid: 8 May 2023

Digital Object Identifier: 10.2969/aspm/08810491

Subjects:
Primary: 11B57
Secondary: 13F60

Keywords: Calkin–Wilf tree , cluster algebra , one-punctured torus , Stern–Brocot tree

Rights: Copyright © 2023 Mathematical Society of Japan

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