Catalog of dessins d'enfants with \le 4 edges

Abstract

In this work all the dessins d'enfant with no more than 4 edges are listed and their Belyi pairs are computed. In order to enumerate all dessins the technique of matrix model computations was used. The total number of dessins is 134; among them 77 are spherical, 53 of genus 1 and 4 of genus 2. The orders of automorphism groups of all the dessins are also found. Dessins are listed by the number of edges. Dessins with the same number of edges are ordered lexicographically by their lists of 0-valencies. The corresponding matrix model for any list of 0-valencies is given and computed. Complex matrix models for dessins with 1 -- 3 edges are used. For the dessins with 4 edges we use Hermitian matrix model, correlators for which are computed in [1].

64 pages, 134 figures

References in corpus (1)

• Partition Functions of Matrix Models as the First Special Functions of String Theory I. Finite Size Hermitean 1-Matrix Model

Cited by in corpus (11)

• Complete Set of Cut-and-Join Operators in Hurwitz-Kontsevich Theory
• On KP-integrable Hurwitz functions
• Cut and join operator ring in Aristotelian tensor model
• Combinatorics of loop equations for branched covers of sphere
• From Kronecker to tableau pseudo-characters in tensor models
• Gauge Theories and Dessins d'Enfants: Beyond the Torus
• On Products of Random Matrices
• Hurwitz numbers from Feynman diagrams
• A Database of Belyi Maps
• Correspondence between Feynman diagrams and operators in quantum field theory that emerges from tensor model
• Genus One Belyi Maps by Quadratic Correspondences