A determinantal formula for cluster variables in cluster algebras from surfaces
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908630414000128 |
|---|---|
| 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 |