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

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

Research output: Contribution to journalArticle

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 pages20
JournalEuropean Journal of Combinatorics
Volume81
Early online date17 Jun 2019
DOIs
Publication statusPublished - Oct 2019

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Sandpile Model
Bijection
Tableaux
Permutation
Configuration
Graph in graph theory
Intransitive
Breadth-first Search
Classify

Keywords

  • math.CO
  • COMPLETE BIPARTITE GRAPH
  • PARALLELOGRAM POLYOMINOES

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

The Abelian sandpile model on Ferrers graphs - A classification of recurrent configurations. / Dukes, Mark; Selig, Thomas; Smith, Jason P.; Steingrimsson, Einar.

In: European Journal of Combinatorics, Vol. 81, 10.2019, p. 221-241.

Research output: Contribution to journalArticle

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