2 problems

Dual-partition refinement conjecture. If $|H_i|\geqslant2$ for all $i\in\Omega$, then the dual partition of $\mathcal{Q}(\boldsymbol{H},\boldsymbol{P})$ is finer than…

Fourier-reflexivity characterization. If $|H_i|\geqslant2$ for all $i\in\Omega$ and $\mathcal{Q}(\boldsymbol{H},\boldsymbol{P})$ is Fourier-reflexive, then $\boldsymbol{P}$ is hier…