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arXiv · 0801.2958

The Z^d Alpern multi-tower theorem for rectangles: a tiling approach

Ayse A. Sahin
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Abstract

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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Ayse A. Sahin. 2008-01-18. The Z^d Alpern multi-tower theorem for rectangles: a tiling approach. https://arxiv.org/abs/0801.2958

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