Virasoro constraints and topological recursion for Grothendieck's dessin counting

Maxim Kazarian, Peter Zograf

We compute the number of coverings of $\mathbb{C}{P}^1\setminus \{0,1,\infty \}$ with a given monodromy type over $\infty$ and given numbers of preimages of 0 and 1. We show that t…