%0 Journal Article
%T The Z^d Alpern multi-tower theorem for rectangles: a tiling approach
%A Ayse A. Sahin
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0801.2958v1