Cluster duality between Calkin-Wilf tree and Stern-Brocot tree
Number Theory
2022-10-11 v3
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 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.
Keywords
Cite
@article{arxiv.2009.06473,
title = {Cluster duality between Calkin-Wilf tree and Stern-Brocot tree},
author = {Yasuaki Gyoda},
journal= {arXiv preprint arXiv:2009.06473},
year = {2022}
}
Comments
21 pages, Addition of relation diagram for each theorem in Introduction, deletion of proof of Theorem 5.3 (1) (switch to paper citation), deletion of Lemma 5.4 and Corollary 5.5, correction of grammatical errors