Arnaud Dartois ; Clémence Magnien
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Results and conjectures on the Sandpile Identity on a lattice
dmtcs:2308 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2003,
DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03)
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https://doi.org/10.46298/dmtcs.2308
Results and conjectures on the Sandpile Identity on a latticeArticle
Authors: Arnaud Dartois 1; Clémence Magnien 1
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Arnaud Dartois;Clémence Magnien
1 Laboratoire d'informatique de l'École polytechnique [Palaiseau]
In this paper we study the identity of the Abelian Sandpile Model on a rectangular lattice.This configuration can be computed with the burning algorithm, which, starting from the empty lattice, computes a sequence of configurations, the last of which is the identity.We extend this algorithm to an infinite lattice, which allows us to prove that the first steps of the algorithm on a finite lattice are the same whatever its size.Finally we introduce a new configuration, which shares the intriguing properties of the identity, but is easier to study.
Matthias Schulz, Lecture Notes in Computer Science, Measures for Transient Configurations of the Sandpile-Model, pp. 238-247, 2006, 10.1007/11861201_29.