Local-to-Global Principles for the Hitting Sequence of a Rotor Walk
Author(s)
Giacaglia, Giuliano Pezzolo; Levine, Lionel; Propp, James; Zayas-Palmer, Linda
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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.
Date issued
2012-01Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Electronic Journal of Combinatorics
Publisher
Electronic Journal of Combinatorics
Citation
Giacaglia, Giuliano Pezzolo, Lionel Levine, James Propp, and Linda Zayas-Palmer. "Local-to-Global Principles for the Hitting Sequence of a Rotor Walk." Electronic Journal of Combinatorics, Volume 19, Issue 1 (2012).
Version: Final published version
ISSN
1077-8926