## Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001

### Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.)

### DMTCS Conference Volume AA (2001), pp. 229-244

author: | Clémence Magnien, Ha Duong Phan and Laurent Vuillon |
---|---|

title: | Characterization of Lattices Induced by (extended) Chip Firing Games |

keywords: | Chip Firing Game, Lattice, Discrete Dynamical Model, Sand Pile Model |

abstract: | The Chip Firing Game (CFG) is a
discrete dynamical model used in physics, computer science
and economics. It is known that the set of configurations
reachable from an initial configuration (this set is called
the configuration space) can be ordered as a lattice.
We first present a structural result about this model, which
allows us to introduce some useful tools for describing those
lattices. Then we establish that the class of lattices that
are the configuration space of a CFG is strictly between the
class of distributive lattices and the class of upper locally
distributive (or ULD) lattices. Finally we propose an
extension of the model, the coloured Chip Firing Game,
which generates exactly the class of ULD lattices. |

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reference: | Clémence Magnien and Ha
Duong Phan and Laurent Vuillon (2001), Characterization of
Lattices Induced by (extended) Chip Firing Games, in
Discrete Models: Combinatorics, Computation, and
Geometry, DM-CCG 2001, Robert Cori and Jacques Mazoyer
and Michel Morvan and Rémy Mosseri (eds.),
Discrete Mathematics and Theoretical Computer Science
Proceedings AA, pp. 229-244 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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