A new method in the combinatorics of the topological expansion

We reduce the counting problem for the vacuum diagrams of a PHI4 theory to a moment problem. As a consequence we are able to give generating function for the counting of diagrams on a torus with one hole, besides the known result for planar diagrams. The method can be extended to PHIsup(n) theory and also to the counting of diagrams on a torus with an arbitrary number of holes. (orig.)