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Dessins d'enfants for analysts

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.

preprint2015arXivOpen access
Vincent Beffara
math.CVmath.NT
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Vincent Beffara

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