Dukes, M., Selig, T., Smith, J.P. ORCID: 0000-0002-4209-1604 and Steingrímsson, E., 2019. The Abelian sandpile model on Ferrers graphs — a classification of recurrent configurations. European Journal of Combinatorics, 81, pp. 221-241. ISSN 0195-6698
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Abstract
We classify all recurrent configurations of the Abelian sandpile model (ASM) on Ferrers graphs. The classification is in terms of decorations of EW-tableaux, which undecorated are in bijection with the minimal recurrent configurations. We introduce decorated permutations, extending to decorated EW-tableaux a bijection between such tableaux and permutations, giving a direct bijection between the decorated permutations and all recurrent configurations of the ASM. We also describe a bijection between the decorated permutations and the intransitive trees of Postnikov, the breadth-first search of which corresponds to a canonical toppling of the corresponding configurations.
Item Type: | Journal article | ||||||||
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Publication Title: | European Journal of Combinatorics | ||||||||
Creators: | Dukes, M., Selig, T., Smith, J.P. and Steingrímsson, E. | ||||||||
Publisher: | Elsevier | ||||||||
Date: | October 2019 | ||||||||
Volume: | 81 | ||||||||
ISSN: | 0195-6698 | ||||||||
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Divisions: | Schools > School of Science and Technology | ||||||||
Record created by: | Linda Sullivan | ||||||||
Date Added: | 22 Apr 2021 14:45 | ||||||||
Last Modified: | 17 Jan 2022 12:46 | ||||||||
URI: | https://irep.ntu.ac.uk/id/eprint/42745 |
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