
TL;DR
This paper introduces an algorithmic approach for exactly computing Belyi functions and dessins d'enfants for hypermaps and triangulations in genus 0 or 1, enabling analysis of larger graphs with minimal algebraic geometry.
Contribution
It presents a novel numerical iterative method combined with lattice reduction for computing Belyi functions, expanding applicability to larger graphs compared to previous methods.
Findings
Applicable to larger graphs than previous methods
Uses minimal algebraic geometry, making it more accessible
Provides a self-contained approach for computing dessins d'enfants
Abstract
We present an algorithmic way of exactly computing Belyi functions for hypermaps and triangulations in genus 0 or 1, and the associated dessins, based on a numerical iterative approach initialized from a circle packing combined with subsequent lattice reduction. The main advantage compared to previous methods is that it is applicable to much larger graphs; we use very little algebraic geometry, and aim for this paper to be as self-contained as possible.
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Taxonomy
TopicsPsychotherapy Techniques and Applications · Psychoanalysis and Psychopathology Research · Educational Philosophies and Pedagogies
