1 Laboratoire d'informatique Algorithmique : Fondements et Applications
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.
Source : ScholeXplorer
IsRelatedTo DOI 10.5772/35757
10.5772/35757
10.5772/35757
Poly-Dimension of Antimatroids
4 Documents citing this article
Source : OpenCitations
Ha, Le Manh; Tam, Nguyen Anh; Duong, Phan Thi Ha, 2010, Algorithmic Aspects Of The Reachability Of Conflicting Chip Firing Game, Advances In Intelligent Information And Database Systems, pp. 359-370, 10.1007/978-3-642-12090-9_31.
Habib, Michel; Nourine, Lhouari, 2018, Representation Of Lattices Via Set-Colored Posets, Discrete Applied Mathematics, 249, pp. 64-73, 10.1016/j.dam.2018.03.068.
Pham, Trung Van; Phan, Thi Ha Duong, 2013, Lattices Generated By Chip Firing Game Models: Criteria And Recognition Algorithms, European Journal Of Combinatorics, 34, 5, pp. 812-832, 10.1016/j.ejc.2012.12.008.