$q$-rationals and dimers

Fuente: arXiv
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Main Author: Ovsienko, Valentin
Format: Preprint
Published: 2025
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author Ovsienko, Valentin
author_facet Ovsienko, Valentin
contents We describe the relationships between the notion of $q$-deformed rational numbers, introduced in our previous work with Sophie Morier-Genoud, and the theory of dimer models. We show that $q$-deformed rationals can be calculated in terms of perfect matchings of certain bipartite graphs, known as snake graphs, or ribbon tiles, etc. equipped with a certain weight function on the set of edges. We apply some elements of the dimer theory to get more information about $q$-rationals.
format Preprint
id arxiv_https___arxiv_org_abs_2510_16270
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle $q$-rationals and dimers
Ovsienko, Valentin
Combinatorics
We describe the relationships between the notion of $q$-deformed rational numbers, introduced in our previous work with Sophie Morier-Genoud, and the theory of dimer models. We show that $q$-deformed rationals can be calculated in terms of perfect matchings of certain bipartite graphs, known as snake graphs, or ribbon tiles, etc. equipped with a certain weight function on the set of edges. We apply some elements of the dimer theory to get more information about $q$-rationals.
title $q$-rationals and dimers
topic Combinatorics
url https://arxiv.org/abs/2510.16270