Tiling Lattices with Sublattices, I

Details Tiling Lattices with Sublattices, I Tiling Lattices with Sublattices, I

2009-05-04

arxiv.org/abs/0905.0441v2

Mathematics

Combinatorics

1 page, 0 figures

Scientific paper

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.

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