FPM 2007, vol. 13, no. 6, pp. 137-148

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 6, PAGES 137-148

The computation of Belyi pairs of $6$ -edged dessins d'enfants of genus $3$ with automorphism groups of order $12$ and $3$

B. S. Bychkov
V. A. Dremov
E. M. Epifanov

Abstract

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In this article, we study dessins d'enfants of genus three with six edges and only one vertex, having group of automorphisms of order at least three. We find all such dessins and explain the method of the enumeration. For each of them the Belyi pair is computed.

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The computation of Belyi pairs of 6-edged dessins d'enfants of genus 3 with automorphism groups of order 12 and 3

The computation of Belyi pairs of $6$ -edged dessins d'enfants of genus $3$ with automorphism groups of order $12$ and $3$