Characterization of Lattices Induced by extended Chip Firing GamesReport as inadecuate

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1 LIAFA - Laboratoire d-informatique Algorithmique : Fondements et Applications

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 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.

Keywords : Sand Pile Model Discrete Dynamical Model Lattice Chip Firing Game

Author: Clémence Magnien - Ha Duong Phan - Laurent Vuillon -



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