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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.24237 |
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| _version_ | 1866910250671538176 |
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| author | Kirillov, Anatol Kostov, Ivan |
| author_facet | Kirillov, Anatol Kostov, Ivan |
| contents | The genus--g Fuss--Catalan (FC) number counts the number of ways to obtain a genus-g surface by identifying the edges of a pn--gon via p-valent hyperedges. For p=2 these are the genus--g Catalan numbers which are generated as the trace correlations in the Gaussian matrix model (GUE). Here we construct a simple two-matrix model which generates the higher-genus Fuss--Catalan numbers for any p as the coefficients of its 1/N-expansion. We obtain exact sum rules and an explicit formula for the higher-genus Fuss--Catalan numbers which generalises the Harer--Zagier formula to p>2. We discuss the relation of the higher-genus FC numbers to the intersection numbers and the Euler characteristic of the moduli space of spin-p curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24237 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Matrix Model for Higher-Genus Fuss--Catalan Numbers Kirillov, Anatol Kostov, Ivan High Energy Physics - Theory Mathematical Physics The genus--g Fuss--Catalan (FC) number counts the number of ways to obtain a genus-g surface by identifying the edges of a pn--gon via p-valent hyperedges. For p=2 these are the genus--g Catalan numbers which are generated as the trace correlations in the Gaussian matrix model (GUE). Here we construct a simple two-matrix model which generates the higher-genus Fuss--Catalan numbers for any p as the coefficients of its 1/N-expansion. We obtain exact sum rules and an explicit formula for the higher-genus Fuss--Catalan numbers which generalises the Harer--Zagier formula to p>2. We discuss the relation of the higher-genus FC numbers to the intersection numbers and the Euler characteristic of the moduli space of spin-p curves. |
| title | A Matrix Model for Higher-Genus Fuss--Catalan Numbers |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2605.24237 |