3 problems

Alternating and c-noncrossing face conjecture. If $(\widetilde\beta,\widetilde\gamma)\in\widetilde R$ span a two-dimensional face of the normal fan of $P$, then $(\beta,\gamma)$ mu…

Surjectivity conjecture for generalized W-permutohedra. The maps in Theorem are surjective.

Noncrossing matching ensemble realization conjecture. Every noncrossing matching ensemble appears as ${\mathcal E}(P)$ for some generic simple polypositroid $P$.