Combinatorics and asymptotic behavior for double Hurwitz numbers
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917445654020096 |
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| author | Li, Xiang |
| author_facet | Li, Xiang |
| contents | Polynomial-in-time algorithms for computing classical Hurwitz numbers were given in [4] based on the Pandharipande equation. The paritition function of double Hurwitz numbers was proved [21] to satisfy the 2-Toda hierarchy. In this paper, similar to [21] we derive Pandharipande-type equations for double Hurwitz numbers from 2-Toda hierarchy. Based on these equations and a method from [4], we study large genus as well as large degree asymptotics of double Hurwitz numbers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_26323 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Combinatorics and asymptotic behavior for double Hurwitz numbers Li, Xiang Mathematical Physics Combinatorics Polynomial-in-time algorithms for computing classical Hurwitz numbers were given in [4] based on the Pandharipande equation. The paritition function of double Hurwitz numbers was proved [21] to satisfy the 2-Toda hierarchy. In this paper, similar to [21] we derive Pandharipande-type equations for double Hurwitz numbers from 2-Toda hierarchy. Based on these equations and a method from [4], we study large genus as well as large degree asymptotics of double Hurwitz numbers. |
| title | Combinatorics and asymptotic behavior for double Hurwitz numbers |
| topic | Mathematical Physics Combinatorics |
| url | https://arxiv.org/abs/2604.26323 |