Results and conjectures on the Sandpile Identity on a latticeReport as inadecuate

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1 LIX - Laboratoire d-informatique de l-École polytechnique Palaiseau

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.

Keywords : Abelian sandpile Identity Burning algorithm Infinite lattice Toppling

Author: Arnaud Dartois - Clémence Magnien -



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