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- W1977210009 abstract "Branched covers of the complex projective line ramified over $0,1$ and $infty$ (Grothendieck's {em dessins d'enfant}) of fixed genus and degree are effectively enumerated. More precisely, branched covers of a given ramification profile over $infty$ and given numbers of preimages of $0$ and $1$ are considered. The generating function for the numbers of such covers is shown to satisfy a PDE that determines it uniquely modulo a simple initial condition. Moreover, this generating function satisfies an infinite system of PDE's called the KP (Kadomtsev-Petviashvili) hierarchy. A specification of this generating function for certain values of parameters generates the numbers of {em dessins} of given genus and degree, thus providing a fast algorithm for computing these numbers." @default.
- W1977210009 created "2016-06-24" @default.
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- W1977210009 date "2013-12-09" @default.
- W1977210009 modified "2023-09-27" @default.
- W1977210009 title "Enumeration of Grothendieck's dessins and KP hierarchy" @default.
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