Mathematical Research Letters

Volume 7 (2000)

Number 4

Toda equations for Hurwitz numbers

Pages: 447 – 453



Andrei Okounkov (University of California at Berkeley)


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.

Full Text (PDF format)