DMTCS Proceedings, Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001

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DMTCS Conference vol AA (2001), pp. 329-340

DMTCS

Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001

Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.)

DMTCS Conference Volume AA (2001), pp. 329-340


author: Alexander Zvonkin
title: Megamaps: Construction and Examples
keywords: Riemann surface; ramified covering; dessins d'enfants; Belyi function; braid group; Hurwitz scheme
abstract: We consider the usual model of hypermaps or, equivalently, bipartite maps, represented by pairs of permutations that act transitively on a set of edges
E
. The specific feature of our construction is the fact that the elements of
E
are themselves (or are labelled by) rather complicated combinatorial objects, namely, the 4-constellations, while the permutations defining the hypermap originate from an action of the Hurwitz braid group on these 4-constellations. The motivation for the whole construction is the combinatorial representation of the parameter space of the ramified coverings of the Riemann sphere having four ramification points.
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reference: Alexander Zvonkin (2001), Megamaps: Construction and Examples, in Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AA, pp. 329-340
bibtex: For a corresponding BibTeX entry, please consider our BibTeX-file.
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