Mathematical Research Letters

Volume 7, Issue 4, July 2000 pp. 447-453.

Toda equations for Hurwitz numbers

Authors: Andrei Okounkov
Author institution: University of California Berkeley

Summary: 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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