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Results and conjectures on the Sandpile Identity on a lattice
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03), DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03) (2003).

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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.
DOI : 10.46298/dmtcs.2308
Classification : 05C70 
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     author = {Dartois, Arnaud and Magnien, Cl\'emence},
     title = {Results and conjectures on the {Sandpile} {Identity} on a lattice},
     journal = {Discrete mathematics & theoretical computer science},
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Dartois, Arnaud; Magnien, Clémence. Results and conjectures on the Sandpile Identity on a lattice. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03), DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03) (2003). doi : 10.46298/dmtcs.2308. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2308/

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