Qureshi–Rinaldo–Romeo conjecture on simple polyominoes

Let $cmathcal{P}$ be a simple polyomino, meaning a polyomino without holes, and let $K[cmathcal{P}]$ be its associated coordinate ring. Qureshi–Rinaldo–Romeo conjecture. The switching rook polynomial of $cmathcal{P}$ coincides with the $h$-polynomial of $K[cmathcal{P}]$. This conjecture is a special case of the broader correspondence considered in the paper; it was proposed for simple polyominoes and remains open in the supplied source.