The Abelian sandpile model on Ferrers graphs -- A classification of recurrent configurations
Combinatorics
2019-06-27 v2
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.
Keywords
Cite
@article{arxiv.1809.07728,
title = {The Abelian sandpile model on Ferrers graphs -- A classification of recurrent configurations},
author = {Mark Dukes and Thomas Selig and Jason P. Smith and Einar Steingrimsson},
journal= {arXiv preprint arXiv:1809.07728},
year = {2019}
}