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Discrete Mathematics & Theoretical Computer Science |
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.
Source : ScholeXplorer
IsRelatedTo ARXIV cond-mat/0303100 Source : ScholeXplorer IsRelatedTo DOI 10.1023/b:joss.0000013960.83555.7d Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.cond-mat/0303100
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