Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Dynamical Systems
Sandpiles, Spanning Trees, And Plane Duality, Melody Chan, Darren B. Glass, Matthew Macauley, David Perkinson, Caryn Werner, Qiaoyu Yang
Sandpiles, Spanning Trees, And Plane Duality, Melody Chan, Darren B. Glass, Matthew Macauley, David Perkinson, Caryn Werner, Qiaoyu Yang
Math Faculty Publications
Let G be a connected, loopless multigraph. The sandpile group of G is a finite abelian group associated to G whose order is equal to the number of spanning trees in G. Holroyd et al. used a dynamical process on graphs called rotor-routing to define a simply transitive action of the sandpile group of G on its set of spanning trees. Their definition depends on two pieces of auxiliary data: a choice of a ribbon graph structure on G, and a choice of a root vertex. Chan, Church, and Grochow showed that if G is a planar ribbon graph, it …