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

Dukes, M, Selig, T, Smith, JP ORCID: https://orcid.org/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:	Number Type 10.1016/j.ejc.2019.05.008 DOI S0195669819300629 Publisher Item Identifier 1390747 Other
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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