Discrete Models: Combinatorics, Computation, and Geometry, DMCCG 2001
Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.)
DMTCS Conference Volume AA (2001), pp. 329340
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
4constellations, while the permutations defining the
hypermap originate from an action of the Hurwitz braid
group on these 4constellations. 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, DMCCG 2001, Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AA, pp. 329340 
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