Shilei Fan

activity

20242026

collaborators

6 papers

math.CA2026

Weak Tiling by Unions of Non-overlapping Unit Cubes

Tianyu Chen, Shilei Fan, Mihail N. Kolountzakis +1

We study weak tiling by finite unions of pairwise non-overlapping unit cubes in $R^{d}$ that are not necessarily axis-parallel. We obtain a weak-tiling analogue of Keller's c…

math.CA2026

Translational tiles without spectra in finite abelian p-groups

Shilei Fan, Mamateli Kadir

We construct explicit translational tiles without spectra in three finite abelian $p$ -groups. The first is a $64$ -point subset of $Z_{4}^{4} \times Z_{2}^{2}$ . The other two are a $512$ -po…

math.FA2026

The optimal hypercontractive constants for $Z_{3}$ and biased Bernoulli random variables

Jie Cao, Shilei Fan, Yong Han +2

We resolve a folklore problem of determining the optimal hypercontractive constants $r_{p, q} (Z_{3})$ for the cyclic group $Z_{3}$ for all $1 < p < q < \infty$ . More p…

math.CA2025

Tiling the field $Q_{p}$ of $p$ -adic numbers by a function

Shilei Fan

This study explores the properties of the function which can tile the field $Q_{p}$ of $p$ -adic numbers by translation. It is established that functions capable of tiling $\…

math.CA2024

The structure of tiles in $Z_{p^{n}} \times Z_{q}$ and $Z_{p^{n}} \times Z_{p}$

Shilei Fan, Mamateli Kadir, Peishan Li

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…

math.GR2024

Periodicity of tiles in finite Abelian groups

Shilei Fan, Tao Zhang

In this paper, we introduce the periodic tiling (PT) property for finite abelian groups. A finite abelian group is said to have the PT property if every non-periodic set that tiles…

Weak Tiling by Unions of Non-overlapping Unit Cubes

Translational tiles without spectra in finite abelian p-groups

The optimal hypercontractive constants for Z3​ and biased Bernoulli random variables

Tiling the field Qp​ of p-adic numbers by a function

The structure of tiles in Zpn​×Zq​ and Zpn​×Zp​

Periodicity of tiles in finite Abelian groups

The optimal hypercontractive constants for $Z_{3}$ and biased Bernoulli random variables

Tiling the field $Q_{p}$ of $p$ -adic numbers by a function

The structure of tiles in $Z_{p^{n}} \times Z_{q}$ and $Z_{p^{n}} \times Z_{p}$