By David Feldman and others

We use Fourier methods to prove that if *n > 1* translates of sublattices of *Z^d* tile *Z^d*, and all the sublattices are Cartesian products of arithmetic progressions, then two of the tiles must be translates of each other. This is a multi-dimensional generalization of the Mirsky-Newman Theorem.

June 3, 2010

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Tiling Lattices with Sublattices, I

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