Tiling Lattices with Sublattices, I

2009/05/04 by David Feldman, James Propp, Feldman, David +3
Mathematics · #52C10 #52C22 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:52C10 #msc:52C22

paper · pdf · doi:10.48550/arxiv.0905.0441

1 page, 0 figures

arxiv created 2010/06/03 · arxiv updated 2010/06/04

Abstract

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.

Related

• Tiling Lattices with Sublattices, II
• Tiling the integer lattice with translated sublattices
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