Local-to-Global Principles for the Hitting Sequence of a Rotor Walk
Name
Giacaglia-2012-Local-to-global principles.pdf
Size
414.22 KB
Format
Adobe PDF
Checksum (MD5)
10d0c380c81cb93fe5cf2e12708c159b
Author(s)
Giacaglia, Giuliano Pezzolo
Levine, Lionel
Propp, James
Zayas-Palmer, Linda
Date Issued
January 2012
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.37236/12
