4 papers · 1 filter
Complete non-ambiguous trees and associated permutations: new enumerative results
Thomas Selig, Haoyue Zhu
We study a link between complete non-ambiguous trees (CNATs) and permutations exhibited by Daniel Chen and Sebastian Ohlig in recent work. In this, they associate a certain permuta…
Prime graphical parking functions and strongly recurrent configurations of the Abelian sandpile model
Thomas Selig, Haoyue Zhu
This work investigates the duality between two discrete dynamical processes: parking functions, and the Abelian sandpile model (ASM). Specifically, we are interested in the extensi…
Parking functions and Åukasiewicz paths
Thomas Selig, Haoyue Zhu
We present a bijection between two well-known objects in the ubiquitous Catalan family: non-decreasing parking functions and Åukasiewicz paths. This bijection maps the maximal dis…
Abelian and stochastic sandpile models on complete bipartite graphs
Thomas Selig, Haoyue Zhu
In the sandpile model, vertices of a graph are allocated grains of sand. At each unit of time, a grain is added to a randomly chosen vertex. If that causes its number of grains to…