Megamaps: Construction and examples. (English) Zbl 1007.05099
Discrete models: combinatorics, computation, and geometry. Proceedings of the 1st international conference (DM-CCG), Paris, France, July 2-5, 2001. Paris: Maison de l’Informatique et des Mathématiques Discrètes (MIMD), Discrete Math. Theor. Comput. Sci., Proc. AA, 329-340, electronic only (2001).
Summary: 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.
For the entire collection see [Zbl 0985.00015].
For the entire collection see [Zbl 0985.00015].
MSC:
| 05E99 | Algebraic combinatorics |
| 57N12 | Topology of the Euclidean \(3\)-space and the \(3\)-sphere (MSC2010) |
| 57N05 | Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010) |
| 14H55 | Riemann surfaces; Weierstrass points; gap sequences |
