Ivona Puljić: Enumeration of regular maps on the torus

Povzetek. First part of the talk will be dedicated to A. Altschuler's paper entitled 'Construction and enumeration of regular maps on the torus'. A short review of Altschuler's algorithm for counting toroidal regular maps of type {3,6} will be presented. Since toroidal regular maps of type {3,6} and toroidal regular maps of type {6,3} (or toriodal polyhexes - TPHs) are duals, second part of the talk will deal with the algorithm for enumeration of TPHs given by authors Kirby, Mallion and Pollak, and slightly modified by T. Pisanski. The talk will end up with presenting a closed formula which answers to our question and depends only on the number of hexagons in the map.