4 research outputs found
Catalog of dessins d'enfants with \le 4 edges
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].Comment: 64 pages, 134 figure