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arXiv · 2411.02696

The structure of tiles in $\mathbb{Z}_{p^n}\times \mathbb{Z}_q$ and $\mathbb{Z}_{p^n}\times \mathbb{Z}_p$

Shilei Fan·Mamateli Kadir·Peishan Li
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Abstract

In this paper, we provide a geometric characterization of tiles in the finite abelian groups \( \mathbb{Z}_{p^n} \times \mathbb{Z}_q \) and \( \mathbb{Z}_{p^n} \times \mathbb{Z}_p \) using the concept of a \( p \)-homogeneous tree, which provides an intuitively visualizable criterion.

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Shilei Fan, Mamateli Kadir, Peishan Li. 2024-11-05. The structure of tiles in $\mathbb{Z}_{p^n}\times \mathbb{Z}_q$ and $\mathbb{Z}_{p^n}\times \mathbb{Z}_p$. https://arxiv.org/abs/2411.02696

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