A purely combinatorial approach to cluster expansions

The problem of convergence of cluster (Mayer) expansions has a long history, and several different methods were used by various authors to get reasonable estimates. The conclusion of some recent developments seems to be that possibly the most powerful, and at the same time the simplest, method is the purely combinatorial one. I will show the connection of this method with exactly soluble cases (determinants, Ising model) and will also suggest the possibility to apply the method to establish the nonabsolute convergence of some interesting cluster expansion series, appearing in the perturbation theory of masslesss Gaussians.