Maria Del Rio Francos (FMF UL, Slovenija): Medial symmetry type graphs of edege-transitive Maps

Date of publication: 30. 11. 2010
Seminar for group theory and combinatorics
Četrtek, 2. 12. 2010, od 17:15 do 18:15, učilnica 014, Pedagoška fakulteta Univerze v Ljubljani
Povzetek: The topological definition of a map M is given by a 2-cell embedding of a graph on a surface. Drawing the barycentric triangulation of the faces of M, where each triangle represents a flag (a triple of a vertex, an edge and a face, mutually incidents) on the map M. There is a combinatorial definition of a map M, regarding its set of flags, and a set of permutations of this set. We will work with this definition for this talk.
A k-orbit map is a map whose automorphism group partitions the set of flags into k-orbits. It is known that each edge-transitive map is either 1-, 2- or 4-orbit map. Graver, Siran, Tuker and Watkins studied them long time ago showing that there are exactly 14 edge-transitive types of maps. Recently, Orbanic, Pellicer and Weiss, studied the k-orbit maps, for k = 1,2,3,4; classifyng them in 33 types (including the 14 edge-transitive).
In a joined work with Orbanic and Pisanski, we present a tool for classifying this symmetry types of map, by graphs. In particular we determine k-orbit maps that are medials of other and we try to extend this to k = 5,6,7