Tiles and weak tiles in $\mathbb{Z}_{pq}$

Mamateli Kadir; Kaibo Fan

Tiles and weak tiles in $\mathbb{Z}_{pq}$

Classical Analysis and ODEs 2026-07-02 v1

Authors: Mamateli Kadir , Kaibo Fan

Abstract

This paper investigates the relationship between tiles and weak tiles in the context of finite cyclic group $\mathbb{Z}_{pq}$ . We prove that weak tiles and translational tiles are equivalent in this group. Our proof employs Fourier analysis, Delsarte parameters, and the Coven-Meyerowitz conditions.

Cite

@article{arxiv.2607.02149,
  title  = {Tiles and weak tiles in $\mathbb{Z}_{pq}$},
  author = {Mamateli Kadir and Kaibo Fan},
  journal= {arXiv preprint arXiv:2607.02149},
  year   = {2026}
}