Let ${\mathcal P}\subset{\mathbb Z}^2$ 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 $v\in {\mathcal P}$ is uniquely determined by the labeling of all other points in the polygon. We introduce a class of ${\mathbb Z}^2$-shift systems, the {\em polygonal shifts}, determined by such a polygon: these are shift systems such that the restriction of any $x\in X$ to some polygon ${\mathcal P}$ 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 include many other systems. We give necessary conditions for a ${\mathbb Z}^2$-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.

中文翻译：

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多边形Z2子位移

令$ {\ mathcal P} \ subset {\ mathbb Z} ^ 2 $是一个凸多边形，其中每个顶点都用一个有限集合中的元素标记，使得每个顶点$ v \ in在{\ mathcal P中} $由多边形中所有其他点的标签唯一地确定。我们引入一类$ {\ mathbb Z} ^ 2 $移位系统，即{\ em多边形移位}，它由这样的多边形确定：这些移位系统是将X $中的任何$ x \限制为某些多边形$ {\ mathcal P} $具有此属性。这些多边形系统与各种经过广泛研究的移位系统相关，包括有限类型的子移位和代数移位，但还包括许多其他系统。根据$ X $的非扩展子空间，我们给出了$ {\ mathbb Z} ^ 2 $-系统$ X $为多边形的必要条件，