TY - JOUR
T1 - A counterexample to Fuglede’s conjecture in (Z/pZ)
4 for all odd primes
AU - Mattheus, Sam
PY - 2020/1/1
Y1 - 2020/1/1
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.
UR - http://www.scopus.com/inward/record.url?scp=85106822709&partnerID=8YFLogxK
U2 - 10.36045/J.BBMS.190708
DO - 10.36045/J.BBMS.190708
M3 - Article
VL - 27
SP - 481
EP - 488
JO - Bulletin of the Belgian Mathematical Society - Simon Stevin
JF - Bulletin of the Belgian Mathematical Society - Simon Stevin
SN - 1370-1444
IS - 4
ER -