Sandpile model and Tutte polynomials

Yvan Le Borgne

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


A new explicit bijection between spanning trees and recurrent configurations of the sandpile model is given. This mapping is such that the difference between the number of grains on a configuration and the external activity of the associate tree is the number of edges of the graph. It is a bijective proof of a result of Merino-L/'opez that express the generating function of recurrent configurations as an evaluation of the Tutte polynomial.

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