Fuglede's conjecture fails in 4 dimensions over odd prime fields
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Publication:2279258
DOI10.1016/j.disc.2019.04.026zbMath1430.52029arXiv1901.08734OpenAlexW2912918749WikidataQ123252245 ScholiaQ123252245MaRDI QIDQ2279258
Samuel J. Ferguson, Nat Sothanaphan
Publication date: 12 December 2019
Published in: Discrete Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1901.08734
Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)
Related Items (10)
Spectral sets and tiles in \(\mathbb{Z}_p^2 \times \mathbb{Z}_q^2\) ⋮ On the structure of spectral and tiling subsets of cyclic groups ⋮ Tiling and spectrality for generalized Sierpinski self-affine sets ⋮ Fuglede’s Conjecture Holds in \(\boldsymbol{\mathbb{Z}_{p}\times \mathbb{Z}_{p^{n}}}\) ⋮ Unnamed Item ⋮ A counterexample to Fuglede's conjecture in \((\mathbb{Z}/p\mathbb{Z})^4\) for all odd primes ⋮ Fuglede's conjecture holds in \(\mathbb{Q}_p\) ⋮ On Gabor orthonormal bases over finite prime fields ⋮ Fuglede's conjecture holds for cyclic groups of order \(pqrs\) ⋮ Fuglede’s conjecture holds on ℤ_{𝕡}²×ℤ_{𝕢}
Uses Software
Cites Work
- The Fuglede conjecture holds in \(\mathbb{Z}_p\times \mathbb{Z}_p\)
- Complex Hadamard matrices and the spectral set conjecture
- On Fuglede's conjecture and the existence of universal spectra
- Spectral theory of commuting self-adjoint partial differential operators
- Around Rédei's theorem
- Commuting self-adjoint partial differential operators and a group theoretic problem
- Fuglede's conjecture is false in 5 and higher dimensions
- Tiling sets and spectral sets over finite fields
- Tiles with no spectra in dimension 4
- Fuglede’s conjecture fails in dimension 4
- Tiles with no spectra
- Unnamed Item
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