Giacaglia, Giuliano Pezzolo; Levine, Lionel; Propp, James; Zayas-Palmer, Linda Local-to-global principles for the hitting sequence of a rotor walk. (English) Zbl 1243.05105 Electron. J. Comb. 19, No. 1, Research Paper P5, 23 p. (2012). Summary: In rotor walk on a finite directed graph, the exits from each vertex follow a prescribed periodic sequence. Here we consider the case of rotor walk where a particle starts from a designated source vertex and continues until it hits a designated target set, at which point the walk is restarted from the source. We show that the sequence of successively hit targets, which is easily seen to be eventually periodic, is in fact periodic. We show moreover that reversing the periodic patterns of all rotor sequences causes the periodic pattern of the hitting sequence to be reversed as well. The proofs involve a new notion of equivalence of rotor configurations, and an extension of rotor walk incorporating time-reversed particles. Cited in 1 Document MSC: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05C38 Paths and cycles 05C81 Random walks on graphs 05C20 Directed graphs (digraphs), tournaments 90B10 Deterministic network models in operations research Keywords:cycle popping; hitting sequence; monoid action; rotor-router model; sandpile group; sandpile monoid; rotor sequences PDFBibTeX XMLCite \textit{G. P. Giacaglia} et al., Electron. J. Comb. 19, No. 1, Research Paper P5, 23 p. (2012; Zbl 1243.05105) Full Text: arXiv EMIS