Lattices generated by Chip Firing Game models: criteria and recognition algorithm
Abstract
It is wellknown that the class of lattices generated by Chip Firing games (CFGs) is strictly included in the class of upper locally distributive lattices (ULD). However a necessary and sufficient criterion for this class is still an open question. In this paper we settle this problem by giving such a criterion. This criterion provides a polynomialtime algorithm for constructing a CFG which generates a given lattice if such a CFG exists. Going further we solve the same problem on two other classes of lattices which are generated by CFGs on the classes of undirected graphs and directed acyclic graphs.
 Publication:

arXiv eprints
 Pub Date:
 May 2012
 arXiv:
 arXiv:1205.6256
 Bibcode:
 2012arXiv1205.6256V
 Keywords:

 Computer Science  Discrete Mathematics
 EPrint:
 Some informations about the term "Abelian Sandpile model" have been added to this version