The Abelian sandpile model on Ferrers graphs — a classification of recurrent configurations
Dukes, Mark and Selig, Thomas and Smith, Jason P. and Steingrímsson, Einar (2019) The Abelian sandpile model on Ferrers graphs — a classification of recurrent configurations. European Journal of Combinatorics, 81. pp. 221-241. ISSN 0195-6698 (https://doi.org/10.1016/j.ejc.2019.05.008)
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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.
ORCID iDs
Dukes, Mark, Selig, Thomas, Smith, Jason P. and Steingrímsson, Einar ORCID: https://orcid.org/0000-0003-4611-0849;-
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Item type: Article ID code: 69069 Dates: DateEvent31 October 2019Published17 June 2019Published Online23 May 2019AcceptedSubjects: Science > Mathematics Department: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 26 Jul 2019 11:57 Last modified: 23 Sep 2024 00:47 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/69069