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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.14554 |
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| _version_ | 1866908630414000128 |
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| author | De Loera, Javier |
| author_facet | De Loera, Javier |
| contents | For cluster algebras of surface type, Musiker, Schiffler and Williams gave a formula for cluster variables in terms of perfect matchings of snake graphs. Building on this, we provide a simple determinantal formula for cluster variables via the weighted biadjacency matrix of the associated snake graphs, thus circumventing the enumeration of their perfect matchings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A determinantal formula for cluster variables in cluster algebras from surfaces De Loera, Javier Combinatorics 13F60, 05C70, 05C22 For cluster algebras of surface type, Musiker, Schiffler and Williams gave a formula for cluster variables in terms of perfect matchings of snake graphs. Building on this, we provide a simple determinantal formula for cluster variables via the weighted biadjacency matrix of the associated snake graphs, thus circumventing the enumeration of their perfect matchings. |
| title | A determinantal formula for cluster variables in cluster algebras from surfaces |
| topic | Combinatorics 13F60, 05C70, 05C22 |
| url | https://arxiv.org/abs/2410.14554 |