Atsushi Kadowaki

Fuglede's conjecture holds in $\mathbb{F}_2^7$

We prove that a nonempty subset of the binary vector space $\mathbb{F}_2^7$ is spectral if and only if it tiles $\mathbb{F}_2^7$ by translations. This is the smallest binary dimension left open by Ferguson and Sothanaphan. For the implication from tiling to spectrality we show that every eight-point subset of $\mathbb{...