European Journal of Combinatorics
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
Mixing of random walks and other diffusions on a graph
Surveys in combinatorics, 1995
Chip-Firing and the Critical Group of a Graph
Journal of Algebraic Combinatorics: An International Journal
Enumeration of (p, q)-parking functions
Discrete Mathematics
A chip-firing game and Dirichelt eigenvalues
Discrete Mathematics - Kleitman and combinatorics: a celebration
The sand-pile model and Tutte polynomials
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Algorithmic Aspects of a Chip-Firing Game
Combinatorics, Probability and Computing
Chip firing and all-terminal network reliability bounds
Discrete Optimization
On the structure of the h-vector of a paving matroid
European Journal of Combinatorics
Chip-firing games, potential theory on graphs, and spanning trees
Journal of Combinatorial Theory Series A
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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.