Enumerative combinatorics
European Journal of Combinatorics
Games on line graphs and sand piles
Theoretical Computer Science
Chip-Firing Games on Directed Graphs
Journal of Algebraic Combinatorics: An International Journal
A simplified proof for a self-stabilizing protocol: a game of cards
Information Processing Letters
Chip-Firing and the Critical Group of a Graph
Journal of Algebraic Combinatorics: An International Journal
On the sandpile group of dual graphs
European Journal of Combinatorics
Structure of some sand piles model
Theoretical Computer Science
The structure of a linear chip firing game and related models
Theoretical Computer Science
Fundamental study: From sandpiles to sand automata
Theoretical Computer Science
Strict partitions and discrete dynamical systems
Theoretical Computer Science
The 1-color problem and the Brylawski model
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Self-organized combinatorial optimization
Expert Systems with Applications: An International Journal
Kadanoff sand pile model. Avalanche structure and wave shape
Theoretical Computer Science
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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 models and chip firing games. After giving an historical survey of the main results which appeared about this, we propose a unified framework to explain the strong relationship between these models and lattices. In particular, we show that the apparent complexity of these models can be reduced, by showing the possibility of simplifying them, and we show how the known lattice properties can be deduced from this.