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

Mark Dukes, Thomas Selig, Jason P. Smith, Einar Steingrímsson

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)221-241
Number of pages21
JournalEuropean Journal of Combinatorics
Volume81
DOIs
Publication statusPublished - Oct 2019
Externally publishedYes

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