NEW METHOD IN THE COMBINATORICS OF THE TOPOLOGICAL EXPANSION

We reduce the counting problem for the vacuum diagrams of a φ4 theory to a moment problem. As a consequence we are able to give the 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 φn theory and also to the counting of diagrams on a torus with an arbitrary number of holes. © 1979 Springer-Verlag.