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.

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
Mots-clés : Virial expansion, cluster expansion, two-connected graph, involution, Tonks gas, hard-core gas 
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     title = {A solution to the combinatorial puzzle of {Mayer{\textquoteright}s} virial expansion},
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     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/aihpd/18/}
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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. http://archive.numdam.org/articles/10.4171/aihpd/18/

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