Orders of Transient Configurations of the Abelian Sandpile-Model

摘要

The set of transient configurations of the Abelian Sandpile Model (ASM) is considered. We look for partial orders of this set satisfying some "sensible" conditions. Some "natural" partial orders will be given and analyzed and efficient algorithms are presented which enable to check whether one given transient configuration is smaller than another given transient configuration. A large part of this article will be devoted to the analysis of the maximal partial order satisfying the given conditions and its relation to the former given partial orders. Since this maximal partial order generally is not a total order the set of transient configurations generally cannot be totally ordered by an order satisfying the given conditions.