4 problems

Let $M$ be a cosimple gammoid of corank at least two. A positive double circuit is a double circuit whose circuit partition has more singular classes than multiple classes. Positiv…

Let $M$ be a matroid with circuit set $\mathcal{C}$, and suppose that an adjoint of $M$ exists. Let $\delta M^*$ denote the combinatorial derived matroid of the dual matroid. Dual-…

Let $M$ be a matroid with ground-set size $n$ and rank $k$, and let $M^*$ denote its dual. Assume that $M^*$ has an adjoint. Adjoint conjecture. Then $\delta M$ is isomorphic to an…

A $C^A$-free gammoid is a gammoid avoiding the excluded configuration $C^A$. The duality conjecture. The class of $C^A$-free gammoids is closed under duality. This is presented as…