Lattices generated by Chip Firing Game models: criteria and recognition algorithm
Discrete Mathematics
2013-10-10 v3
Abstract
It is well-known 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 polynomial-time 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.
Cite
@article{arxiv.1205.6256,
title = {Lattices generated by Chip Firing Game models: criteria and recognition algorithm},
author = {Trung Van Pham and Thi Ha Duong Phan},
journal= {arXiv preprint arXiv:1205.6256},
year = {2013}
}
Comments
Some informations about the term "Abelian Sandpile model" have been added to this version