Mark Dukes, Thomas Selig, Jason P. Smith, Einar Steingrimsson
Published 2018-09-20Version 1
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.
EW-tableaux, Le-tableaux, tree-like tableaux and the Abelian sandpile model
On the classification of self-dual $\mathbb{Z}_k$-codes II
Abelian sandpile model and Biggs-Merino polynomial for directed graphs
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