Results and conjectures on the Sandpile Identity on a lattice
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 in...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2003-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2308/pdf |
| _version_ | 1797270657236467712 |
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| author | Arnaud Dartois Clémence Magnien |
| author_facet | Arnaud Dartois Clémence Magnien |
| author_sort | Arnaud Dartois |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:07:45Z |
| format | Article |
| id | doaj.art-dcecd76114974c4cb1980f69d3b454ea |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:07:45Z |
| publishDate | 2003-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-dcecd76114974c4cb1980f69d3b454ea2024-03-07T14:28:31ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502003-01-01DMTCS Proceedings vol. AB,...Proceedings10.46298/dmtcs.23082308Results and conjectures on the Sandpile Identity on a latticeArnaud Dartois0Clémence Magnien1Laboratoire d'informatique de l'École polytechnique [Palaiseau]Laboratoire d'informatique de l'École polytechnique [Palaiseau]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://dmtcs.episciences.org/2308/pdfabelian sandpileidentityburning algorithminfinite latticetoppling[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] |
| spellingShingle | Arnaud Dartois Clémence Magnien Results and conjectures on the Sandpile Identity on a lattice Discrete Mathematics & Theoretical Computer Science abelian sandpile identity burning algorithm infinite lattice toppling [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] |
| title | Results and conjectures on the Sandpile Identity on a lattice |
| title_full | Results and conjectures on the Sandpile Identity on a lattice |
| title_fullStr | Results and conjectures on the Sandpile Identity on a lattice |
| title_full_unstemmed | Results and conjectures on the Sandpile Identity on a lattice |
| title_short | Results and conjectures on the Sandpile Identity on a lattice |
| title_sort | results and conjectures on the sandpile identity on a lattice |
| topic | abelian sandpile identity burning algorithm infinite lattice toppling [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] |
| url | https://dmtcs.episciences.org/2308/pdf |
| work_keys_str_mv | AT arnauddartois resultsandconjecturesonthesandpileidentityonalattice AT clemencemagnien resultsandconjecturesonthesandpileidentityonalattice |