The Mathematics of Chip-firing is a solid introduction and overview of the growing field of
chip-firing. It offers an appreciation for the richness and diversity of the subject. Chip-firing …

Chip-Firing and Rotor-Routing on Directed Graphs Page 1 Progress in Probability, Vol. 60,
331–364 ©c 2008 Birkhauser Verlag Basel/Switzerland Chip-Firing and Rotor-Routing on …

Divisors and Sandpiles provides an introduction to the combinatorial theory of chip-firing on
finite graphs. Part 1 motivates the study of the discrete Laplacian by introducing the dollar …

For a graph $ G $, we construct two algebras whose dimensions are both equal to the
number of spanning trees of $ G $. One of these algebras is the quotient of the polynomial …

The notion of parking functions was introduced by Konheim and Weiss [53] as a colorful way
to describe their work on computer storage. The parking problem can be stated as follows …

Let M denote the Laplacian matrix of a graph G. Associated with G is a finite group Φ (G),
obtained from the Smith normal form of M, and whose order is the number of spanning trees …

Starting from some studies of (linear) integer partitions, we noticed that the lattice structure is
strongly related to a large variety of discrete dynamical models, in particular sandpile …

We review the status of the two-dimensional Abelian sandpile model as a strong candidate
to provide a lattice realization of logarithmic conformal invariance with a central charge c …

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 grains …

The critical group of a connected graph is a finite abelian group, whose order is the number
of spanning trees in the graph, and which is closely related to the graph Laplacian. Its group …