Geodesic
The Tutte polynomial as a growth function
Journal of Algebraic Combinatorics, Tome 10 (1999) no. 2, pp. 115-133.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The 'dollar game' represents a kind of diffusion process on a graph. Under the rules of the game some cofigurations are both stable and recurrent, and these are known as critical cofigurations. The set of critical configurations can be given the structure of an abelian group, and it turns out that the order of the group is the tree-number of the graph. Each critical configuration can be assigned a positive weight, and the generating function that enumerates critical configurations according to weight is a partial evaluation of the Tutte polynomial of the graph. It is shown that the weight enumerator can also be interpreted as a growth function, which leads to the conclusion that the (partial) Tutte polynomial itself is a growth function.
Keywords: tutte polynomial, chip-firing, critical group, growth function 
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     title = {The {Tutte} polynomial as a growth function},
     journal = {Journal of Algebraic Combinatorics},
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     url = {http://geodesic.mathdoc.fr/item/JAC_1999__10_2_a4/}
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Biggs, Norman. The Tutte polynomial as a growth function. Journal of Algebraic Combinatorics, Tome 10 (1999) no. 2, pp. 115-133. http://geodesic.mathdoc.fr/item/JAC_1999__10_2_a4/