Rotor-Routing Induces the Only Consistent Sandpile Torsor Structure on Plane Graphs

Abstract

We make precise and prove a conjecture of Klivans about actions of the sandpile group on spanning trees. More specifically, the conjecture states that there exists a unique ‘suitably nice’ sandpile torsor structure on plane graphs which is induced by rotor-routing.

Keywords

• 05E18
• 05C10