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Article Dans Une Revue Seminaire Lotharingien de Combinatoire Année : 2008

Solution to a combinatorial puzzle arising from Mayer's theory of cluster integrals

Olivier Bernardi
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Résumé

Mayer's theory of cluster integrals allows one to write the partition function of a gas model as a generating function of weighted graphs. Recently, Labelle, Leroux and Ducharme have studied the graph weights arising from the one-dimensional hard-core gas model and noticed that the sum of the weights over all connected graphs with $n$ vertices is $(-n)^{n-1}$. This is, up to sign, the number of rooted Cayley trees on $n$ vertices and the authors asked for a combinatorial explanation. The main goal of this article is to provide such an explanation.
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hal-00267999 , version 1 (30-03-2008)

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Olivier Bernardi. Solution to a combinatorial puzzle arising from Mayer's theory of cluster integrals. Seminaire Lotharingien de Combinatoire, 2008, 59, pp.B59e. ⟨hal-00267999⟩
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