Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6871606 | Discrete Applied Mathematics | 2018 | 10 Pages |
Abstract
We define the analogue of linear equivalence of graph divisors for the rotor-router model, and use it to prove polynomial time computability of some problems related to rotor-routing. Using the connection between linear equivalence for chip-firing and for rotor-routing, we give a simple proof for the fact that the number of rotor-router unicycle-orbits equals the order of the Picard group. We also show that the rotor-router action of the Picard group on the set of spanning in-arborescences can be interpreted in terms of the linear equivalence.
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Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Lilla Tóthmérész,