On dessins d'enfants with equal supports
Fedor Pakovich

TL;DR
This paper investigates the conditions under which different dessins d'enfants, associated with Belyi functions ramified over three points, share the same support set on the Riemann sphere.
Contribution
It provides a characterization of when two dessins d'enfants have identical supports, clarifying the relationship between Belyi functions and their underlying support sets.
Findings
Identifies conditions for equal supports of dessins d'enfants
Characterizes the structure of Belyi functions with shared supports
Enhances understanding of dessins d'enfants and their supports
Abstract
For a Belyi function ramified only over the points , a corresponding ``dessin d'enfant'' is defined as the set considered as a bi-colored graph on the Riemann sphere whose white and black vertices are points of the sets and correspondingly. Merely the set without a graph structure is called a support of . In this note, we solve the following problem: under what conditions different dessins and have equal supports?
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Analytic Number Theory Research
