On the recursion formula for double Hurwitz numbers

Author:
Shengmao Zhu

Journal:
Proc. Amer. Math. Soc. **140** (2012), 3749-3760

MSC (2010):
Primary 14H10; Secondary 05E05

DOI:
https://doi.org/10.1090/S0002-9939-2012-11235-3

Published electronically:
March 12, 2012

MathSciNet review:
2944715

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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 -classes.

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Additional Information

**Shengmao Zhu**

Affiliation:
Department of Mathematics and Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, People’s Republic of China

Email:
zhushengmao@gmail.com

DOI:
https://doi.org/10.1090/S0002-9939-2012-11235-3

Keywords:
Hurwitz numbers,
moduli space,
cut-join,
recursion

Received by editor(s):
November 30, 2010

Received by editor(s) in revised form:
April 28, 2011

Published electronically:
March 12, 2012

Communicated by:
Lev Borisov

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.