The chip-firing game

AbstractThe process called the chip-firing game has been around for no more than 20 years, but it has rapidly become an important and interesting object of study in structural combinatorics. The reason for this is partly due to its relation with the Tutte polynomial and group theory, but also because of the contribution of people in theoretical physics who know it as the (Abelian) sandpile model.Here, we survey some of the numerous connections that the chip-firing game has with some other parts of combinatorics and with theoretical physics. Among these we present its relation with the Tutte polynomial, group theory, greedoids with repetition and matroids. We also reintroduce it as the Abelian sandpile model of statistical mechanics and give a relation with the Potts model