A Canonical Group-Like Structure on the Spanning Trees of a Plane Graph
Abstract
In this article, we use the rotor-routing algorithm to reveal a surprising algebraic structure on the spanning trees of a plane graph. We begin with a concrete combinatorial description of how the spanning trees interact. Then, we transition to a more algebraic perspective and explain the sense in which the structure is canonical.
Fields of Study & Subjects
Graph theory and applications
Advanced Graph Theory Research
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- American Mathematical Monthly
- Volume
- 133
- Issue
- 2
- Pages
- 111–127
- Publication date
- 9 January 2026
- Language
- EN