6 problems

Rank-three transversal matroid conjecture. Every rank-$3$ transversal matroid has the half-plane property.

Direct-sum conjecture for transversal q-matroids. The direct sum $M_1\oplus M_2$ is a transversal $q$-matroid with presentation $\mathcal{X}_1\oplus\mathcal{X}_2$.

Let $M$ be a $q$-transversal matroid with a presentation by a system of subspaces. A presentation is minimal if no member can be replaced by a proper subspace while preserving the…

Let $M$ be a $q$-matroid on a vector space $V$, with bar nullity function $\overline{n}$, and let $\mathcal X$ be a system of subspaces of $V$. A q-transversal is a subspace obtain…

Rank-three transversal matroid conjecture. Every transversal matroid of rank $3$ has the half-plane 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…