Monotone orbifold Hurwitz numbers
Abstract
In general, Hurwitz numbers count branched covers of the Riemann sphere with prescribed ramification data, or equivalently, factorisations in the symmetric group with prescribed cycle structure data. In this paper, we initiate the study of monotone orbifold Hurwitz numbers. These are simultaneously variations of the orbifold case and generalisations of the monotone case, both of which have been previously studied in the literature. We derive a cut-and-join recursion for monotone orbifold Hurwitz numbers, determine a quantum curve governing their wave function, and state an explicit conjecture relating them to topological recursion.
Keywords
Cite
@article{arxiv.1505.06503,
title = {Monotone orbifold Hurwitz numbers},
author = {Norman Do and Maksim Karev},
journal= {arXiv preprint arXiv:1505.06503},
year = {2015}
}
Comments
Submitted to the Embedded Graphs (St. Petersburg, October 2014) conference proceedings. Changed text to improve readability; added references; extended Lemma 7 and proof; added statement of monotone ELSV formula