Geodesic
A solution to the combinatorial puzzle of Mayer’s virial expansion
Annales de l’Institut Henri Poincaré D, Tome 2 (2015) no. 3, pp. 229-262

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Mayer’s second theorem in the context of a classical gasmodel allows us to write the coe�fficients 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)!. Th�is paper addresses the question of achieving a purely combinatorial proof of this observation and extends the proof of Bernardi for the connected graph case.

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DOI : 10.4171/aihpd/18
Classification : 82-XX, 05-XX
Keywords: Virial expansion, cluster expansion, two-connected graph, involution, Tonks gas, hard-core gas 
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Tate, Stephen James. A solution to the combinatorial puzzle of Mayer’s virial expansion. Annales de l’Institut Henri Poincaré D, Tome 2 (2015) no. 3, pp. 229-262. doi: 10.4171/aihpd/18

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