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

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

2008-03-31

arxiv.org/abs/0803.4386v1

Seminaire Lotharingien de Combinatoire 59 (2008) B59e

Mathematics

Combinatorics

9 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Solution to a combinatorial puzzle arising from Mayer's theory of cluster integrals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Solution to a combinatorial puzzle arising from Mayer's theory of cluster integrals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Solution to a combinatorial puzzle arising from Mayer's theory of cluster integrals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-197083