4 problems

Domino-stability conjecture. The ring $K[\mathcal{P}]$ is Gorenstein if and only if $\mathcal{P}$ is domino-stable.

Rinaldo–Romeo conjecture. The polyomino $\mathcal{P}$ is thin if and only if

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 switch…

Let $\mathcal{P}$ be a collection of cells. The Gorenstein characterization conjecture asserts that the following are equivalent: 1. $K[\mathcal{P}]$ is Gorenstein; 2. the $h$-poly…