Geodesic
Graph weights arising from Mayer and Ree-Hoover theories of virial expansions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008).

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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. 
@article{DMTCS_2008_special_255_a54,
     author = {Kaouche, Amel and Leroux, Pierre},
     title = {Graph weights arising from {Mayer} and {Ree-Hoover} theories of virial expansions},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)},
     year = {2008},
     doi = {10.46298/dmtcs.3646},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3646/}
}
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Kaouche, Amel; Leroux, Pierre. Graph weights arising from Mayer and Ree-Hoover theories of virial expansions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008). doi : 10.46298/dmtcs.3646. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3646/

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