## Alexander Zvonkin - Megamaps: Construction and Examples

dmtcs:2284 - Discrete Mathematics & Theoretical Computer Science, January 1, 2001, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001) - https://doi.org/10.46298/dmtcs.2284
Megamaps: Construction and Examples

Authors: Alexander Zvonkin

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.

Volume: DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)
Section: Proceedings
Published on: January 1, 2001
Imported on: November 21, 2016
Keywords: Riemann surface,ramified covering,dessins d'enfants,Belyi function,braid group,Hurwitz scheme,[INFO] Computer Science [cs],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]