Revisiting Groeneveld’s approach to the virial expansion

A generalized version of Groeneveld's convergence criterion for the virial expansion and generating functionals weighted $2$-connected graphs is proven. The works inhomogeneous systems yields bounds density expansions correlation functions $\rho_s$ (a.k.a. distribution or factorial moment measures) grand-canonical Gibbs measures with pairwise interactions. proof based on recurrence relations graph weights related to Kirkwood-Salsburg integral equation functions. does not use an inversion density-activity expansion, however a Moebius lattice set partitions enters derivation relations.