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Amel Kaouche ; Pierre Leroux - Graph weights arising from Mayer and Ree-Hoover theories of virial expansions

dmtcs:3646 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3646
Graph weights arising from Mayer and Ree-Hoover theories of virial expansionsConference paper

Authors: Amel Kaouche 1; Pierre Leroux 1

  • 1 Laboratoire de combinatoire et d'informatique mathématique [Montréal]

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 wM(c) and the Ree-Hoover weight wRH(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.


Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: graph invariants,non-ideal gas,hard sphere gas,Mayer weights,virial expansion.,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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