Pairs of tree dessins, their Shabat polynomials, and monodromy groups
Algebraic Geometry
2025-10-14 v1 Combinatorics
Group Theory
Abstract
Coverings of the Riemann sphere by itself, ramified over two points, are given by so-called Shabat polynomials. The correspondence between Grothendieck's dessins d'enfants and Belyi maps then implies a bijection between Shabat polynomials and tree dessins (bicolored plane trees). Dessins can be assigned a combinatorial invariant known as their passport, which records the degrees of their vertices. We consider all possible passports determining a pair of tree dessins, determining the associated Shabat polynomials and monodromy groups.
Keywords
Cite
@article{arxiv.2510.10192,
title = {Pairs of tree dessins, their Shabat polynomials, and monodromy groups},
author = {Benjamin Dupont and Revekka Kyriakoglou and Vassilis Metaftsis and Efstratios Prassidis and Alexandros Singh},
journal= {arXiv preprint arXiv:2510.10192},
year = {2025}
}
Comments
30 pages, 16 figures