9 problems

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

Representability conjecture for coordinate q-matroids. If the corresponding matroid of a coordinate $q$-matroid is representable, then the $q$-matroid is representable.

Asymptotic counting conjecture. For each prime power $q$, we have

Asymptotic counting conjecture. For all $r\geq 2$ and prime powers $q$, we have

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…

Circuit-cocircuit intersection conjecture. Under these hypotheses, Definition is an equivalence relation.

Dual equivalence-relation conjecture. The relation of Definition is an equivalence relation in at least one of $M$ and $M^*$.

Conjectured convolution-inverse formula. For the relevant indices $a,b,c,d$,