hide
Free keywords:
Mathematics, Combinatorics, Mathematical Physics, Algebraic Geometry
Abstract:
We prove quasi-polynomiality for monotone and strictly monotone orbifold Hurwitz numbers. The second enumerative problem is also known as enumeration of a special kind of Grothendieck's dessins d'enfants or $r$-hypermaps. These statements answer positively two conjectures proposed by Do-Karev and Do-Manescu. We also apply the same method to the usual orbifold Hurwitz numbers
and obtain a new proof of the quasi-polynomiality in this case. In the second part of the paper we show that the property of
quasi-polynomiality is equivalent in all these three cases to the property that the $n$-point generating function has a natural representation on the $n$-th cartesian powers of a certain algebraic curve. These representations are the
necessary conditions for the Chekhov-Eynard-Orantin topological recursion.
