矩形的Z^d Alpern多塔定理：一种平铺方法
The Z^d Alpern multi-tower theorem for rectangles: a tiling approach
摘要：
我们给出了关于Z^d作用的Alpern多塔定理的一个证明。我们将该定理重新表述为一个问题，即通过一组矩形来可测地平铺Z^d作用量的轨道，这些矩形的对应边没有非平凡的公因数。我们关联到这样一个集合的矩形一个特殊的家庭广义多米诺骨牌平铺。然后，我们确定了一个内在的动态特性，这些平铺，视为象征性的动力系统，它允许一个多塔分解。
英文摘要：
We provide a proof of the Alpern multi-tower theorem for Z^d actions. We reformulate the theorem as a problem of measurably tiling orbits of a Z^d action by a collection of rectangles whose corresponding sides have no non-trivial common divisors. We associate to such a collection of rectangles a special family of generalized domino tilings. We then identify an intrinsic dynamic property of these tilings, viewed as symbolic dynamical systems, which allows for a multi-tower decomposition.
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