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Results and conjectures on the Sandpile Identity on a lattice

Abstract : 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.
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Arnaud Dartois, Clémence Magnien. Results and conjectures on the Sandpile Identity on a lattice. Discrete Models for Complex Systems, DMCS'03, 2003, Lyon, France. pp.89-102, ⟨10.46298/dmtcs.2308⟩. ⟨hal-01183316⟩



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