Virial Expansion Bounds Through Tree Partition Schemes

In this paper, we use tree partition schemes and an algebraic expression for the virial coefficients in terms of the cluster coefficients in order to derve upper bounds on the virial coefficients and consequently lower bounds on the radius of convergence of the virial expansion $\mathcal{R}_{\textrm{Vir}}$. The bound on the radius of convergence in the case of the Penrose partition scheme is the same as that proposed by Groeneveld and improves the bound achieved by Lebowitz and Penrose.