Ribbon decomposition and twisted Hurwitz numbers
Combinatorics
2022-01-28 v3 Algebraic Geometry
Abstract
Ribbon decomposition is a way to obtain a surface with boundary (compact, not necessarily oriented) from a collection of disks by joining them with narrow ribbons attached to segments of the boundary. Counting ribbon decompositions gives rise to a "twisted" version of the classical Hurwitz numbers (studied earlier in \cite{CD} in a different context) and of the cut-and-join equation. We also provide an algebraic description of these numbers and an explicit formula for them in terms of zonal polynomials.
Keywords
Cite
@article{arxiv.2107.13861,
title = {Ribbon decomposition and twisted Hurwitz numbers},
author = {Yurii Burman and Raphaël Fesler},
journal= {arXiv preprint arXiv:2107.13861},
year = {2022}
}
Comments
21 pages, 4 figures. v2 : The previous version of the paper was revised (including correction of some theorems) and completely rewritten ; v3 : minor corrections