Characterization of Lattices Induced by (extended) Chip Firing Games
Magnien, Clémence ; Phan, Ha Duong ; Vuillon, Laurent
HAL, hal-01182957 / Harvested from HAL
Text on HAL
The Chip Firing Game (CFG) is a discrete dynamical model used in physics, computer science and economics. It is known that the set of configurationsreachable from an initial configuration (this set is called the \textitconfiguration 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 \textitcoloured Chip Firing Game, which generates exactly the class of ULD lattices.
Publié le : 2001-07-04
Classification:  Sand Pile Model,  Discrete Dynamical Model,  Lattice,  Chip Firing Game,  [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],  [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],  [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG] 
@article{hal-01182957,
     author = {Magnien, Cl\'emence and Phan, Ha Duong and Vuillon, Laurent},
     title = {Characterization of Lattices Induced by (extended) Chip Firing Games},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01182957}
}

Magnien, Clémence; Phan, Ha Duong; Vuillon, Laurent. Characterization of Lattices Induced by (extended) Chip Firing Games. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-01182957/