Annales de l’Institut Henri Poincaré D

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Volume 2, Issue 3, 2015, pp. 229–262
DOI: 10.4171/AIHPD/18

Published online: 2015-08-28

A solution to the combinatorial puzzle of Mayer’s virial expansion

Stephen James Tate[1]

(1) Imperial College London, UK

Mayer’s second theorem in the context of a classical gasmodel allows us to write the coefficients of the virial expansion of pressure in terms of weighted two-connected graphs. Labelle, Leroux and Ducharme studied the graph weights arising from the one-dimensional hardcore gas model and noticed that the sum of these weights over all two-connected graphs with $n$ vertices is $–n(n–2)!$. This paper addresses the question of achieving a purely combinatorial proof of this observation and extends the proof of Bernardi for the connected graph case.

Keywords: Virial expansion, cluster expansion, two-connected graph, involution, Tonks gas, hard-core gas

Tate Stephen James: A solution to the combinatorial puzzle of Mayer’s virial expansion. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 2 (2015), 229-262. doi: 10.4171/AIHPD/18