Shabat Polynomials and Monodromy Groups of Trees Uniquely Determined by their Passport
Number Theory
2019-05-29 v1
Abstract
A dessin d'enfant, or dessin, is a bicolored graph embedded into a Riemann surface. Acyclic dessins can be described analytically by pre-images of certain polynomials, called Shabat polynomials, and also algebraically by their monodromy groups, that is, the group generated by rotations of edges about black and white vertices. In this paper we investigate the Shabat polynomials and monodromy groups of planar acyclic dessins that are uniquely determined by their passports.
Keywords
Cite
@article{arxiv.1805.07530,
title = {Shabat Polynomials and Monodromy Groups of Trees Uniquely Determined by their Passport},
author = {Naiomi Cameron and Mary Kemp and Susan Maslak and Gabrielle Melamed and Richard A. Moy and Jonathan Pham and Austin Wei},
journal= {arXiv preprint arXiv:1805.07530},
year = {2019}
}