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Mamateli Kadir

Publications and source records attributed to Mamateli Kadir.

5 recordsLinked to original sources
arXiv2026

Translational tiles without spectra in finite abelian p-groups

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 $512$-point subset of $\F_2^{13}$ and a $2187$-point subset of $\F_3^9$. Consequently, the tile-to-spectral implication fails for finite abelian $p$-groups, and it already fails within the class of elementary abelian groups for both $p=2$ and $p=3$. Two elementary mechanisms organize the examples. A two-layer obstruction turns a spectral non-tile with two suitable tiling complements into a tile without a spectrum. A fiber--clique obstruction converts a family of tiling complements with controlled common Fourier zeros into an elementary abelian counterexample. All coordinate data are included. The finite claims are certified by three short, self-contained programs using exact integer arithmetic and exhaustive searches; the accompanying source files recompute every assertion used in the proofs.

math.CA↗
arXiv2026

A characterization of compact open spectral sets in $\mathbb{Q}_p^d$

Let $Ω\subset \Qp^d$ be a compact open set. Such a set, without lose of generality, admits a representation \(Ω= \bigsqcup_{c \in C} (c + p^n\Zp^d)\), where $C \subset (\Z/p^n\Z)^d$ and $n \in\N$. We prove that $Ω$ tiles $\Qp^d$ by translation if and only if $C$ tiles $(\Z/p^n\Z)^d$ by translation. Moreover, $Ω$ is a spectral set in $\Qp^d$ if and only if $C$ is a spectral set in $(\Z/p^n\Z)^d$.

math.CA↗
arXiv2026

On product spectral sets and functional tiles in $\mathbb{Q}_p^d$

This paper studies product spectral sets and functional tiles in the $p$-adic spaces $\mathbb{Q}_p^d$ within the framework of the {\bf product spectral set conjecture}. We establish a stability result for functional tiles under weak convergence of tiling complements, characterize product spectral pairs with product spectra, and fully resolve the conjecture for cylindric sets by proving that spectrality of a cylindric set $Ω=B_γ(a)\timesΘ$ is equivalent to spectrality of $Θ$.

math.GM↗
arXiv2026

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

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.

math.CA↗