On the recursion formula for double Hurwitz numbers (Q2846729)
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scientific article; zbMATH DE number 6204247
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the recursion formula for double Hurwitz numbers |
scientific article; zbMATH DE number 6204247 |
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On the recursion formula for double Hurwitz numbers (English)
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3 September 2013
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Hurwitz numbers
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moduli space of curves
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cut-join
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recursion
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The double Hurwitz number counts branched covers of \(\mathbb P^1\) branched at \(0\) and \(\infty\) with prescribed ramification orders. Certain generating function of double Hurwitz numbers satisfies a differential equation, called the cut-join equation. In the paper under review, the author establishes a recursion formula for double Hurwitz numbers using some combinatorial cut-join analysis. As an application, the author also obtains a polynomial identity and a recursion formula for certain conjectural intersection numbers of Hodge integral type proposed by \textit{I. P. Goulden, D. M. Jackson} and \textit{R. Vakil} [Adv. Math. 198, No. 1, 43--92 (2005; Zbl 1086.14022)].
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