TY - JOUR
T1 - The Abelian sandpile model on Ferrers graphs — a classification of recurrent configurations
AU - Dukes, Mark
AU - Selig, Thomas
AU - Smith, Jason P.
AU - Steingrímsson, Einar
PY - 2019/10/31
Y1 - 2019/10/31
N2 - 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.
AB - 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.
KW - Abelian sandpile model
KW - EW-tableaux
KW - Ferrers graph
UR - http://www.scopus.com/inward/record.url?scp=85067260076&partnerID=8YFLogxK
U2 - 10.1016/j.ejc.2019.05.008
DO - 10.1016/j.ejc.2019.05.008
M3 - Article
AN - SCOPUS:85067260076
SN - 0195-6698
VL - 81
SP - 221
EP - 241
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
ER -