## Discrete Models for Complex Systems, DMCS'03

### Michel Morvan and Éric Rémila (eds.)

### DMTCS Conference Volume AB (2003), pp. 89-102

author: | Arnaud Dartois and Clémence Magnien |
---|---|

title: | Results and conjectures on the Sandpile Identity on a lattice |

keywords: | Abelian sandpile, Identity, Burning algorithm, Infinite lattice, Toppling |

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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reference: | Arnaud Dartois and
Clémence Magnien (2003), Results and conjectures on
the Sandpile Identity on a lattice, in Discrete Models
for Complex Systems, DMCS'03, Michel Morvan and
Éric Rémila (eds.), Discrete Mathematics
and Theoretical Computer Science Proceedings AB, pp.
89-102 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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