Tiling and weak tiling in (ℤ_p)^d

2022/12/11 by Gergely Kiss, Dávid Matolcsi, Kiss, Gergely +5
Materials Science · Mathematics · Computer Science · #Quasicrystal Structures and Properties #Mathematical Analysis and Transform Methods #Cellular Automata and Applications

paper · pdf · doi:10.48550/arxiv.2212.05513

Abstract

We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary p-groups (ℤ_p)^d, we introduce an averaging procedure that leads to a natural object of study: a 4-tuple of functions which can be regarded as a common generalization of tiles and spectral sets. We characterize such 4-tuples for d=1, 2, and prove some partial results for d=3.

Related

• Spectrality of Prime Size Tiles
• Periodicity of tiles in finite Abelian groups
• Tiling sets and spectral sets over finite fields
• The structure of tiles in ℤ_pⁿ× ℤ_q and ℤ_pⁿ× ℤ_p
• Functions tiling with several lattices