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Toda equations for Hurwitz numbers

Andrei Okounkov
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Abstract

We consider ramified coverings of P^1 with arbitrary ramification type over 0 and infinity 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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Andrei Okounkov. 2000-04-19. Toda equations for Hurwitz numbers. https://arxiv.org/abs/math/0004128

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