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november 2020 A counterexample to Fuglede's conjecture in $(\mathbb{Z}/p\mathbb{Z})^4$ for all odd primes
Sam Mattheus
Bull. Belg. Math. Soc. Simon Stevin 27(4): 481-488 (november 2020). DOI: 10.36045/j.bbms.190708

Abstract

We construct a spectral, non-tiling set of size $2p$ in $\mathbb Z/p\mathbb Z{4}$, $p$ odd prime. This example complements a previous counterexample in [C. Aten et al., \textit{Tiling sets and spectral sets over finite fields}, arXiv:1509.01090], which existed only for $p \equiv 3 \pmod{4}$. On the contrary we show that the conjecture does hold in $(\mathbb Z/2\mathbb Z)^4$.

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Sam Mattheus. "A counterexample to Fuglede's conjecture in $(\mathbb{Z}/p\mathbb{Z})^4$ for all odd primes." Bull. Belg. Math. Soc. Simon Stevin 27 (4) 481 - 488, november 2020. https://doi.org/10.36045/j.bbms.190708

Information

Published: november 2020
First available in Project Euclid: 20 November 2020

MathSciNet: MR4177387
Digital Object Identifier: 10.36045/j.bbms.190708

Subjects:
Primary: 05A18, 05B45, 43A25, 51E20, 52C22

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 4 • november 2020
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