The Abelian sandpile model on Ferrers graphs — a classification of recurrent configurations

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
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
Identifiers:
NumberType
10.1016/j.ejc.2019.05.008DOI
S0195669819300629Publisher Item Identifier
1390747Other
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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