2 problems

Let $\mathbf{a}=(a_1,\ldots,a_n)$ be a weak composition, and let $\mathcal{P}(\mathbb{D}(\mathbf{a}))$ be the Kohnert poset of its key diagram. Pattern characterization conjecture.…

Let $D$ be a diagram, let $\mathcal{P}(D)$ be its Kohnert poset, and let $\mathcal{F}$ be a finite collection of families of subdiagrams. Finite forbidden-subdiagram conjecture. Th…