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Multispecies Virial Expansions

We study the virial expansion of mixtures of countably many different types of particles. The main tool is the Lagrange-Good inversion formula, which has other applications such as counting coloured trees or studying probability generating functions in multi-type branching processes. We prove that the virial expansion converges absolutely in a domain of small densities. In addition, we establish that the virial coefficients can be expressed in terms of two-connected graphs.