Classes of Lattices Induced by Chip Firing (and Sandpile) Dynamics

Details Classes of Lattices Induced by Chip Firing (and Sandpile) Dynamics Classes of Lattices Induced by Chip Firing (and Sandpile) Dynamics

2002-01-15

arxiv.org/abs/math/0201131v1

Mathematics

Combinatorics

see also http://www.liafa.jussieu.fr/~magnien

Scientific paper

In this paper we study three classes of models widely used in physics, computer science and social science: the Chip Firing Game, the Abelian Sandpile Model and the Chip Firing Game on a mutating graph. We study the set of configurations reachable from a given initial configuration, called the configuration space of a model, and try to determine the main properties of such sets. We study the order induced over the configurations by the evolution rule. This makes it possible to compare the power of expression of these models. It is known that the configuration spaces we obtain are lattices, a special kind of partially ordered set. Although the Chip Firing Game on a mutating graph is a generalization of the usual Chip Firing Game, we prove that these models generate exactly the same configuration spaces. We also prove that the class of lattices induced by the Abelian Sandpile Model is strictly included in the class of lattices induced by the Chip Firing Game, but contains the class of distributive lattices, a very well known class.

Affiliated with

Also associated with

No associations

Rating

Classes of Lattices Induced by Chip Firing (and Sandpile) Dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classes of Lattices Induced by Chip Firing (and Sandpile) Dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classes of Lattices Induced by Chip Firing (and Sandpile) Dynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-554139