3 papers
math.CO2018
Permutation graphs and the Abelian sandpile model, tiered trees and non-ambiguous binary trees
Mark Dukes, Thomas Selig, Jason P. Smith +1
A permutation graph is a graph whose edges are given by inversions of a permutation. We study the Abelian sandpile model (ASM) on such graphs. We exhibit a bijection between recurr…
math.CO2018
The Abelian sandpile model on Ferrers graphs -- A classification of recurrent configurations
Mark Dukes, Thomas Selig, Jason P. Smith +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…
math.CO2012
A natural stochastic extension of the sandpile model on a graph
Yao-ban Chan, Jean-François Marckert, Thomas Selig
We introduce a new model of a stochastic sandpile on a graph containing a sink. When unstable, a site sends one grain to each of its neighbours independently with probability $…