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arXiv · 2509.23752

Spectrality of Prime Size Tiles

Weiqi Zhou
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Abstract

We prove that if a tile in $\mathbb Z^d$ has prime size $p$, then it must be spectral. The proof is by contradiction, it is simply shown that the tiling complement of such a tile can not annihilate all $p$-subgroups. In addition, with a simple transformation we prove that any $p$ points in general linear positions in $\mathbb Z^d (d\ge p-1)$ must be both tiling and spectral.

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Weiqi Zhou. 2025-09-28. Spectrality of Prime Size Tiles. https://arxiv.org/abs/2509.23752

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