Virasoro Constraints and Topological Recursion for Grothendieck's Dessin Counting
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 (KadomtsevPetviashvili) hierarchy and satisfies a topological recursion in the sense of EynardOrantin.
 Publication:

Letters in Mathematical Physics
 Pub Date:
 August 2015
 DOI:
 10.1007/s1100501507710
 arXiv:
 arXiv:1406.5976
 Bibcode:
 2015LMaPh.105.1057K
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 22 pages, 4 figures