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

Font Size:  Small  Medium  Large

Characterization of Lattices Induced by (extended) Chip Firing Games

Clémence Magnien, Ha Duong Phan, Laurent Vuillon


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.

Full Text: GZIP Compressed PostScript PostScript PDF original HTML abstract page

Valid XHTML 1.0 Transitional