The sand-pile model and Tutte polynomials

Bidimensional Sand Pile Model

In this paper we introduce the Bidimensional Sand Pile Model (BSPM), that is, a generalization of the Sand Pile Model (SPM) with the addition of a further dimension. The SPM and some related models have been studied in many different domains and they play an important role in the theory of discrete dynamical systems. They were considered in the context of integer lattices by Brylawski in 1973. ...

Chain polynomials and Tutte polynomials

The recently introduced chain and sheaf polynomials of a graph are shown to be essentially equivalent to a weighted version of the Tutte polynomial. c © 2002 Elsevier Science B.V. All rights reserved.

Tutte Polynomials and Link Polynomials

We show how the Tutte polynomial of a plane graph can be evaluated as the "homfly" polynomial of an associated oriented link. Then we discuss some consequences for the partition function of the Potts model, the Four Color Problem and the time complexity of the computation of the homfly polynomial.

Tutte Polynomials of Flower Graphs

Structure of some sand pile model

spm (Sand Pile Model) is a simple discrete dynamical system used in physics to represent granular objects. It is deeply related to integer partitions, and many other combinatorics problems, such as tilings or rewriting systems. The evolution of the system started with n stacked grains generates a lattice, denoted by SPM(n). We study here the structure of this lattice. We first explain how it ca...