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arXiv · 2604.26323

Combinatorics and asymptotic behavior for double Hurwitz numbers

Xiang Li
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Abstract

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.

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Xiang Li. 2026-04-29. Combinatorics and asymptotic behavior for double Hurwitz numbers. https://arxiv.org/abs/2604.26323

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