Abstract
The virial expansion, in statistical mechanics, makes use of the sums of the Mayer weights of all 2-connected graphs on \(n\) vertices, for \(n > 1\). A recent trend in discrete mathematics deals with the exact or asymptotic approximation of the Mayer weight of particular graphs or of special families of graphs, starting from their combinatorial structure. In the present work, we use Fourier transforms and spanning (rooted) trees of graphs to develop methods for the computation of these weights in dimensions \(d > 0\), for various families of graphs.
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