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arXiv · 2212.05513

Tiling and weak tiling in $(\mathbb{Z}_p)^d$

Gergely Kiss·Dávid Matolcsi·Máté Matolcsi·Gábor Somlai
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Abstract

We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary $p$-groups $(\mathbb{Z}_p)^d$, 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 $d=3$.

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Gergely Kiss, Dávid Matolcsi, Máté Matolcsi, Gábor Somlai. 2022-12-11. Tiling and weak tiling in $(\mathbb{Z}_p)^d$. https://arxiv.org/abs/2212.05513

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