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  1. Home > Articles & Issues >
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  3. Results and conjectu ...
Conference paper

Results and conjectures on the Sandpile Identity on a lattice

Arnaud Dartois (1), Clémence Magnien ORCID (1)
(1) Laboratoire d'informatique de l'École polytechnique [Palaiseau]
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Imported on
November 21, 2016
Published on
December 31, 2002
Last modified on
March 31, 2025
Volume 0
DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03)
Proceedings
DOI
10.46298/dmtcs.2308
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https://about.hal.science/hal-authorisation-v1
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Results and conjectures on the Sandpile Identity on a lattice

Arnaud Dartois (1), Clémence Magnien ORCID (1)
(1) 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
  • [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]
  • Abelian sandpile
  • Identity
  • Burning algorithm
  • Infinite lattice
  • Toppling
Mathematics Subject Classification 2020
  • 05C70 - Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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