Volumes of moduli spaces of directed ribbon graphs and Cut-and-Join operators

Fuente: arXiv
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Main Author: Barazer, Simon
Format: Preprint
Published: 2025
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author Barazer, Simon
author_facet Barazer, Simon
contents In this paper, we investigate the algebraic structure underlying the acyclic decomposition. This decomposition applies to directed metric ribbon graphs and enables the recursive computation of the volumes of their moduli spaces. Building on this, we define integral operators with these volumes and show that they satisfy a Cut-and-Join type equation. Furthermore, we demonstrate that a suitable specialization of these operators gives rise to a generating series for \textit{dessins d'enfants}.
format Preprint
id arxiv_https___arxiv_org_abs_2507_07308
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Volumes of moduli spaces of directed ribbon graphs and Cut-and-Join operators
Barazer, Simon
Combinatorics
In this paper, we investigate the algebraic structure underlying the acyclic decomposition. This decomposition applies to directed metric ribbon graphs and enables the recursive computation of the volumes of their moduli spaces. Building on this, we define integral operators with these volumes and show that they satisfy a Cut-and-Join type equation. Furthermore, we demonstrate that a suitable specialization of these operators gives rise to a generating series for \textit{dessins d'enfants}.
title Volumes of moduli spaces of directed ribbon graphs and Cut-and-Join operators
topic Combinatorics
url https://arxiv.org/abs/2507.07308