$q$-rationals and dimers
Combinatorics
2025-10-21 v1
Abstract
We describe the relationships between the notion of -deformed rational numbers, introduced in our previous work with Sophie Morier-Genoud, and the theory of dimer models. We show that -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 -rationals.
Cite
@article{arxiv.2510.16270,
title = {$q$-rationals and dimers},
author = {Valentin Ovsienko},
journal= {arXiv preprint arXiv:2510.16270},
year = {2025}
}
Comments
17 pages, 14 figures