On the recursion formula for double Hurwitz numbers

Zhu, Shengmao

doi:10.1090/S0002-9939-2012-11235-3

On the recursion formula for double Hurwitz numbers
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Proc. Amer. Math. Soc. 140 (2012), 3749-3760 Request permission

Abstract:

In this paper, we will give a recursion formula for double Hurwitz numbers by the cut-join analysis. This recursion formula can be considered as a generalized version of the recursion formula for simple Hurwitz numbers derived by Mulase and Zhang. As a direct application, we get a polynomial identity for Goulden-Jackson-Vakil’s conjectural intersection numbers and an explicit recursion formula for the computation of these intersection numbers with only $\psi$-classes.

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