Polygonal Z2‐subshifts
John Franks, Bryna Kra · Proceedings of the London Mathematical Society · 2020
Let P ⊂ Z 2 be a convex polygon with each vertex in it labeled by an element from a finite set and such that the labeling of each vertex v ∈ P is uniquely determined by the labeling of all other points in the polygon. We introduce a class of Z 2 -shift systems, the polygonal shifts, determined by such a polygon: These are shift systems such that the restriction of any x ∈ X to some polygon P has this property. These polygonal systems are related to various well-studied classes of shift systems, including subshifts of finite type and algebraic shifts, but also many other systems. We give necessary conditions for a Z 2 -system X to be polygonal, in terms of the nonexpansive subspaces of X, and under further conditions can give a complete characterization for such systems.