Rotor-routing orbits in directed graphs and the Picard group


In [5], Holroyd, Levine, Mészáros, Peres, Propp and Wilson characterize recurrent chip-and-rotor configurations for strongly connected digraphs. However, the number of steps needed to recur, and the number of orbits is left open for general digraphs. Recently, these questions were answered by Pham [6], using linear algebraic methods. We give new, purely… (More)