Polygonal Z2-subshifts

Let (Formula presented.) 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 (Formula presented.) is uniquely determined by the labeling of all other points in the polygon. We introduce a class of (Formula presented.) -shift systems, the polygonal shifts, determined by such a polygon: These are shift systems such that the restriction of any (Formula presented.) to some polygon (Formula presented.) 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 (Formula presented.) -system (Formula presented.) to be polygonal, in terms of the nonexpansive subspaces of (Formula presented.), and under further conditions can give a complete characterization for such systems.