The structure of tiles in ℤ_pⁿ× ℤ_q and ℤ_pⁿ× ℤ_p

2024/11/05 by Fan, Shilei, Kadir, Mamateli, Li, Peishan
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.02696

Abstract

In this paper, we provide a geometric characterization of tiles in the finite abelian groups \( ℤ_pⁿ × ℤ_q \) and \( ℤ_pⁿ × ℤ_p \) using the concept of a \( p \)-homogeneous tree, which provides an intuitively visualizable criterion.

Related

• Tiling and weak tiling in (ℤ_p)^d
• Combinatorial and harmonic-analytic methods for integer tilings
• The structure of translational tilings in ℤ^d
• A counterexample to the periodic tiling conjecture (announcement)
• Tiling with arbitrary tiles