A representation of virial coefficients that avoids the asymptotic catastrophe (Q1417321)

The notion of an asymptotic catastrophe in the representation of Mayer coefficients is given. Virial-coefficient representations that are free of such catastrophe phenomena are recalled. Sets of labeled graphs (blocks), nonseparable in Harari sense, are introduced and shown to be in relation to the physical problem. Their expansion into classes labeled by cycle ensembles that satisfy specific conditions are given, the representations are based on these expansions. The frames are introduced from cycle ensembles, this gives the possibility to introduce block classification and the use of tree classification of cycle ensembles. Then it is proven, that the described virial-coefficient representations are free of the asymptotic catastrophe phenomenon.