A generalization of rotation of binary sequences and its applications to toggle dynamical systems
arXiv:1909.01125
Abstract
We study a simple generalization of the rotation (or circular shift) of the binary sequences. In particular, we show each orbit of this generalized rotation has a certain statistical symmetry. This generalized rotation naturally arises when we generalize the results of Joseph and Roby on a toggle dynamical system whose state space consists of independent sets on the path graphs.