Rotor-Routing and Spanning Trees on Planar Graphs

  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},
  • M. Chan, Thomas E. Church, Joshua A. Grochow
  • Published 2015
  • Mathematics
  • International Mathematics Research Notices
  • 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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    Publications referenced by this paper.
    Handbook of Combinatorics
    • 1,062
    Self-organized critical state of sandpile automaton models.
    • Dhar
    • Physics, Medicine
    • 1990
    • 635
    Abelian Networks I. Foundations and Examples
    • 32
    • Highly Influential
    • PDF
    Chip-Firing and the Critical Group of a Graph
    • 248
    • PDF
    Embeddings and minors
    • 54
    In and Out of Equilibrium 2
    • 30
    What is the sandpile torsor?
    • 2011