The sand-pile model and Tutte polynomials

Authors:
Robert Cori;Yvan Le Borgne
Affiliations:
Labri, Université Bordeaux 1, 351 Cours de la Libération, 33405 Talence cedex, France;Labri, Université Bordeaux 1, 351 Cours de la Libération, 33405 Talence cedex, France
Venue:
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Year:
2003

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Abstract

A new explicit bijection between spanning trees and recurrent configurations of the sand-pile model is given. This mapping is such that the difference between the number of gains on a configuration and the external activity of the associate tree is the number of edges of the graph. It gives a bijective proof of a result of Merino López expressing the generating function of recurrent configurations as an evaluation of the Tutte polynomial.