On enumeration of $b$-angulations of surfaces from an integrability perspective
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914516162314240 |
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| author | Garcia-Failde, Elba Xu, Jianghao Yang, Di Zagier, Don |
| author_facet | Garcia-Failde, Elba Xu, Jianghao Yang, Di Zagier, Don |
| contents | In this paper, we study generating series enumerating polygonal angulations of closed oriented surfaces of fixed genus, focusing on $b$-angulations with $b = 3$ or $b = 2ν$, $ν\geq 2$. Based on Toda integrability, we establish new structural results in the cases $b = 3$ and $b = 4$. Furthermore, via the Hodge--GUE correspondence, we derive a fine structure in the $b = 2ν$ case, which implies a conjectural statement of Gharakhloo--Latimer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26354 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On enumeration of $b$-angulations of surfaces from an integrability perspective Garcia-Failde, Elba Xu, Jianghao Yang, Di Zagier, Don Mathematical Physics Exactly Solvable and Integrable Systems In this paper, we study generating series enumerating polygonal angulations of closed oriented surfaces of fixed genus, focusing on $b$-angulations with $b = 3$ or $b = 2ν$, $ν\geq 2$. Based on Toda integrability, we establish new structural results in the cases $b = 3$ and $b = 4$. Furthermore, via the Hodge--GUE correspondence, we derive a fine structure in the $b = 2ν$ case, which implies a conjectural statement of Gharakhloo--Latimer. |
| title | On enumeration of $b$-angulations of surfaces from an integrability perspective |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2604.26354 |