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

Mamateli Kadir; Peishan Li; Shilei Fan

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2411.02696 v1 pith:HCT65U5E submitted 2024-11-05 math.CA

Shilei Fan , Mamateli Kadir , Peishan Li This is my paper · ORCID

classification math.CA

keywords mathbbtimestilesabeliancharacterizationconceptcriterionfinite

verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments

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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Tiling the field $\mathbb{Q}_p$ of $p$-adic numbers by a function
math.CA 2024-12 conditional novelty 6.0 of 10

Integrable function tilings of Q_p are uniformly locally constant, yielding a complete answer to Leptin-Müller's question on Q_p and spectrality of tiles in Q_p times Z/2Z.

Pith tools