11 citations · 24 across the 8 of their papers we have counts for
8 papers
The stochastic sandpile model on complete graphs
Thomas Selig
The stochastic sandpile model (SSM) is a generalisation of the standard Abelian sandpile model (ASM), in which topplings of unstable vertices are made random. When unstable, a vert…
Asymptotics of the single-source stochastic sandpile model
Thomas Selig, Haoyue Zhu
In the single-source sandpile model, a number grains of sand are positioned at a central vertex on the 2-dimensional grid . We study the stabilisation of this con…
Combinatorial aspects of sandpile models on wheel and fan graphs
Thomas Selig
We study combinatorial aspects of the sandpile model on wheel and fan graphs, seeking bijective characterisations of the model's recurrent configurations on these families. For whe…
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…
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…
EW-tableaux, Le-tableaux, tree-like tableaux and the Abelian sandpile model
Thomas Selig, Jason P. Smith, Einar Steingrimsson
A EW-tableau is a certain 0/1-filling of a Ferrers diagram, corresponding uniquely to an acyclic orientation, with a unique sink, of a certain bipartite graph called a Ferrers grap…