Properties of Mayer cluster expansion

Abstract

The Umbral algebra developed by Rota and his co-workers is used to show that the Mayer cluster expansion of the canonical partition function is related to the Bell polynomials. The algebra is also used to find a representation of the partition function and a rederivation of Mayer’s first theorem. Finally, it is shown that in the ’’tree approximation’’ for the cluster integrals, the summation of Mayer’s expression for the canonical-ensemble partition function for a finite number of particles could be performed using Dénes’ and Rényi’s theorems in graph theory.