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arXiv · 2109.14179

A Periodicity Result for Tilings of $\mathbb Z^3$ by Clusters of Prime-Squared Cardinality

Abhishek Khetan
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Abstract

We show that if $\mathbb Z^3$ can be tiled by translated copies of a set $F\subseteq\mathbb Z^3$ of cardinality the square of a prime then there is a weakly periodic $F$-tiling of $\mathbb Z^3$, that is, there is a tiling $T$ of $\mathbb Z^3$ by translates of $F$ such that $T$ can be partitioned into finitely many $1$-periodic sets.

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Abhishek Khetan. 2026-06-16. A Periodicity Result for Tilings of $\mathbb Z^3$ by Clusters of Prime-Squared Cardinality. https://arxiv.org/abs/2109.14179

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