A counterexample to Fuglede’s conjecture in (Z/pZ)
            4 for all odd primes

Sam Mattheus

doi:10.36045/J.BBMS.190708

A counterexample to Fuglede’s conjecture in (Z/pZ) ⁴ for all odd primes

Sam Mattheus

Onderzoeksoutput: Article › peer review

6 Citaten (Scopus)

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

Originele taal-2	English
Pagina's (van-tot)	481-488
Aantal pagina's	8
Tijdschrift	Bulletin of the Belgian Mathematical Society - Simon Stevin
Volume	27
Nummer van het tijdschrift	4
DOI's	https://doi.org/10.36045/J.BBMS.190708
Status	Published - 1 jan 2020

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10.36045/J.BBMS.190708

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title = "A counterexample to Fuglede{\textquoteright}s conjecture in (Z/pZ) 4 for all odd primes",

abstract = "We construct a spectral, non-tiling set of size 2p in (Z/pZ)4, p odd prime. This example complements a previous counterexample in [C. Aten et al., Tiling sets and spectral sets over finite fields, arXiv:1509.01090], which existed only for p ≡ 3 (mod 4). On the contrary we show that the conjecture does hold in (Z/2Z)4.",

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N2 - We construct a spectral, non-tiling set of size 2p in (Z/pZ)4, p odd prime. This example complements a previous counterexample in [C. Aten et al., Tiling sets and spectral sets over finite fields, arXiv:1509.01090], which existed only for p ≡ 3 (mod 4). On the contrary we show that the conjecture does hold in (Z/2Z)4.

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

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DO - 10.36045/J.BBMS.190708

M3 - Article

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JO - Bulletin of the Belgian Mathematical Society - Simon Stevin

JF - Bulletin of the Belgian Mathematical Society - Simon Stevin

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A counterexample to Fuglede’s conjecture in (Z/pZ) 4 for all odd primes

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A counterexample to Fuglede’s conjecture in (Z/pZ) ⁴ for all odd primes