Mathematical Research Letters

Volume 7 (2000)

Number 4

Toda equations for Hurwitz numbers

Pages: 447 – 453

DOI: http://dx.doi.org/10.4310/MRL.2000.v7.n4.a10

Author

Andrei Okounkov (University of California at Berkeley)

Abstract

We consider ramified coverings of $\mathbb{P}^1$ with arbitrary ramification type over $0,\infty\in\mathbb{P}^1$ and simple ramifications elsewhere and prove that the generating function for the numbers of such coverings is a $\tau$-function for the Toda lattice hierarchy of Ueno and Takasaki.

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