MAYER AND REE-HOOVER WEIGHTS OF INFINITE FAMILIES OF 2-CONNECTED GRAPHS
Amel Kaouche, Pierre Leroux · 2009
We study graph weights (i.e., graph invariants) which arise natu- rally in Mayer's theory and Ree-Hoover's theory of virial expansions in the con- text 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 explicit formulas for the values of Mayer weights and Ree-Hoover weights for certain infinite families of 2-connected graphs.