Arnaud Dartois ; Clémence Magnien - 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) - https://doi.org/10.46298/dmtcs.2308
Results and conjectures on the Sandpile Identity on a latticeConference paper

Authors: Arnaud Dartois 1; Clémence Magnien ORCID1


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.

https://doi.org/10.46298/dmtcs.2308
Source: HAL:hal-01183316v1
Volume: DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03)
Section: Proceedings
Published on: January 1, 2003
Imported on: November 21, 2016
Keywords: [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], [NLIN.NLIN-CG]Nonlinear Sciences [physics]/Cellular Automata and Lattice Gases [nlin.CG], [en] Abelian sandpile, Identity, Burning algorithm, Infinite lattice, Toppling

Classifications

Mathematics Subject Classification 20201
Sources:
  • [1] zbMATH Open.

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