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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