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 …

Sand pile model (SPM) is a simple discrete dynamical system used in physics to represent
granular objects. It is deeply related to integer partitions, and many other combinatorics …

Recently Andrews introduced the concept of signed partition: a signed partition is a finite
sequence of integers ak,..., a1, a− 1,..., a− l such that ak≥...≥ a1> 0> a− 1≥...≥ a− l. So far …

Game theory has been applied extensively to interpret and solve the complex and
interrelated practical decision problems. The solution for these problems depends on the …

In this paper, we use a simple discrete dynamical model to study integer partitions and their
lattice. The set of reachable configurations of the model, with the order induced by the …

We introduce natural generalizations of two well-known dynamical systems, the Sand Piles
Model and the Brylawski's model. We describe their order structure, their reachable …

Let r, d≤ n be nonnegative integers. In this paper we study the basic properties of a discrete
dynamical model of signed integer partitions that we denote by S (n, d, r). A generic element …

In this paper we introduce sand automata in order to give a common and useful framework
for the study of most of the models of sandpiles. Moreover we give the possibility to have …

We give a survey of our works on the natural extensions of the well-known Sand Pile Model.
These extensions consist of adding outside grains on random columns, allowing sand …

In this paper we study three classes of models widely used in physics, computer science and
social science: the chip firing game (CFG), the Abelian sandpile model (ASM) and the CFG …