2 problems

Let $Z$ be an $n\times(k+m)$ matrix with positive maximal minors, let $\mathcal{A}_{n,k,m}(Z)$ be its amplituhedron, and let a positroid tile be a tile in a positroid tiling of thi…

Plane-partition tiling conjecture. For even $m$, the number of top-dimensional strata in a tiling of $\mathcal{A}_{n,k,m}(Z)$ is equal to the number of plane partitions contained i…