Virasoro constraints and topological recursion for Grothendieck's dessin counting
Combinatorics
2015-12-15 v3
Abstract
We compute the number of coverings of with a given monodromy type over and given numbers of preimages of 0 and 1. We show that the generating function for these numbers enjoys several remarkable integrability properties: it obeys the Virasoro constraints, an evolution equation, the KP (Kadomtsev-Petviashvili) hierarchy and satisfies a topological recursion in the sense of Eynard-Orantin.
Keywords
Cite
@article{arxiv.1406.5976,
title = {Virasoro constraints and topological recursion for Grothendieck's dessin counting},
author = {Maxim Kazarian and Peter Zograf},
journal= {arXiv preprint arXiv:1406.5976},
year = {2015}
}
Comments
22 pages, 4 figures; extended version