# Graph weights arising from Mayer and Ree-Hoover theories of virial expansions

Abstract : We study graph weights (i.e., graph invariants) which arise naturally in Mayer's theory and Ree-Hoover's theory of virial expansions in the context of a non-ideal gas. We give special attention to the Second Mayer weight $w_M(c)$ and the Ree-Hoover weight $w_{RH}(c)$ of a $2$-connected graph $c$ which arise from the hard-core continuum gas in one dimension. These weights are computed using signed volumes of convex polytopes naturally associated with the graph $c$. Among our results are the values of Mayer's weight and Ree-Hoover's weight for all $2$-connected graphs $b$ of size at most $8$, and explicit formulas for certain infinite families.
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https://hal.inria.fr/hal-01185182
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Amel Kaouche, Pierre Leroux. Graph weights arising from Mayer and Ree-Hoover theories of virial expansions. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.259-270, ⟨10.46298/dmtcs.3646⟩. ⟨hal-01185182⟩

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