Abstract
We consider “cubes” in products of finite cyclic groups and we study their tiling and spectral properties. (A set in a finite group is called a tile if some of its translates form a partition of the group and is called spectral if it admits an orhogonal basis of characters for the functions supported on the set.) We show an analog of a theorem due to Iosevich and Pedersen [6], Lagarias, Reeds and Wang [12], and the third author of this paper [8], which identified the tiling complements of the unit cube in Rd with the spectra of the same cube.
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