Combinatorics and asymptotic behavior for double Hurwitz numbers
Mathematical Physics
2026-04-30 v1 Combinatorics
math.MP
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.
Cite
@article{arxiv.2604.26323,
title = {Combinatorics and asymptotic behavior for double Hurwitz numbers},
author = {Xiang Li},
journal= {arXiv preprint arXiv:2604.26323},
year = {2026}
}