vol. 23 no. 1

1. Determining Genus From Sandpile Torsor Algorithms

McDonough, Alex.
We provide a pair of ribbon graphs that have the same rotor routing and Bernardi sandpile torsors, but different topological genus. This resolves a question posed by M. Chan [Cha]. We also show that if we are given a graph, but not its ribbon structure, along with the rotor routing sandpile torsors, we are able to determine the ribbon graph's genus.
Section: Combinatorics