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

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

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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.

Original languageEnglish
Pages (from-to)221-241
Number of pages21
JournalEuropean Journal of Combinatorics
Volume81
Early online date17 Jun 2019
DOIs
Publication statusPublished - 31 Oct 2019

Keywords

  • Abelian sandpile model
  • EW-tableaux
  • Ferrers graph

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