We study graph weights which naturally occur in Mayerâ??s theory and\nRee-Hooverâ??s theory for the virial expansion in the context of an imperfect\ngas. We pay particular attention to the Mayer weight and Ree-Hoover weight\nof a 2-connected graph in the case of the hard-core continuum gas in one dimension.\nThese weights are calculated from signed volumes of convex polytopes\nassociated with the graph. In the present paper, we use the method of\ngraph homomorphisms, to develop other explicit formulas of Mayer weights\nand Ree-Hoover weights for infinite families of 2-connected graphs.
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