A counterexample to Fuglede’s conjecture in (Z/pZ) 4 for all odd primes
Journal Contribution - Journal Article
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.