Cut-and-join equation for monotone Hurwitz numbers revisited
Algebraic Geometry
2019-05-16 v2 Combinatorics
Abstract
We give a new proof of the cut-and-join equation for the monotone Hurwitz numbers, derived first by Goulden, Guay-Paquet, and Novak. Our proof in particular uses a combinatorial technique developed by Han. The main interest in this particular equation is its close relation to the quadratic loop equation in the theory of spectral curve topological recursion, and we recall this motivation giving a new proof of the topological recursion for monotone Hurwitz numbers, obtained first by Do, Dyer, and Mathews.
Keywords
Cite
@article{arxiv.1807.04197,
title = {Cut-and-join equation for monotone Hurwitz numbers revisited},
author = {Petr Dunin-Barkowski and Reinier Kramer and Alexandr Popolitov and Sergey Shadrin},
journal= {arXiv preprint arXiv:1807.04197},
year = {2019}
}
Comments
7 pages. v2: Added a second proof of lemma 2.3, using Jucys-Murphy elements, and expanded motivation