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arXiv · 2009.06473

Cluster duality between Calkin-Wilf tree and Stern-Brocot tree

Yasuaki Gyoda
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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.

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Yasuaki Gyoda. 2020-09-14. Cluster duality between Calkin-Wilf tree and Stern-Brocot tree. https://arxiv.org/abs/2009.06473

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