# Rotor-Routing and Spanning Trees on Planar Graphs

@article{Chan2015RotorRoutingAS, title={Rotor-Routing and Spanning Trees on Planar Graphs}, author={M. Chan and Thomas E. Church and Joshua A. Grochow}, journal={International Mathematics Research Notices}, year={2015}, volume={2015}, pages={3225-3244} }

The sandpile group Pic^0(G) of a finite graph G is a discrete analogue of the Jacobian of a Riemann surface which was rediscovered several times in the contexts of arithmetic geometry, self-organized criticality, random walks, and algorithms. Given a ribbon graph G, Holroyd et al. used the "rotor-routing" model to define a free and transitive action of Pic^0(G) on the set of spanning trees of G. However, their construction depends a priori on a choice of basepoint vertex. Ellenberg asked… CONTINUE READING

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