$q$-rationals and dimers
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911218388697088 |
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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 |