7 problems

A generic $(n,d)$-tropical oriented matroid is a tropical oriented matroid whose associated structures are generic, and an $(n,d)$-matching ensemble is the matching-field encoding…

Let $L$ be a matching field, let $\mathcal I_L$ be its matching field ideal, and consider the collection of all sequences of amalgamations of $L$. Amalgamation conjecture. The coll…

Let $\operatorname{Gr}(k,n)$ be the Grassmannian, and let $M_{\operatorname{Gr}(k,n)}$ be its algebraic matroid. For a coherent matching field $L$, let $M_L$ be the algebraic matro…

Let $B_c^\sigma$ be the matching fields considered in the paper, with $\sigma \in S_n$ and $c \in [p-1]$. Suppose that the matching field polytope associated to $B_c^\sigma$ gives…

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

Polyhedrality conjecture. A left linkage matching field is polyhedral if and only if it satisfies the compatible right submatching property.

Stiefel-map determination conjecture. A linkage matching field is determined by the collection of transversal matroids associated to its maximal tope linkage covectors by the combi…