Tutte seminar - Nick Wormald

Counting Unrooted Maps and Convex Polyhedra

Abstract:

Since the time of Euler, the number of convex polyhedra with a given number of faces, or vertices and faces, has been under investigation. So far, the only results appearing in the literature consist of exhaustive computer generation of each polyhedron. It is well known that the problem is equivalent to counting 3-connected planar maps. In this talk I will discuss old results on the enumeration of unrooted planar maps, as well as a new result with Bob Robinson showing that there is an efficient algorithm for calculating the numbers of convex polyhedra, involving D-finite power series.