8 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…

A positive coline of a matroid is a coline whose copoint partition has more singular classes than multiple classes. A gammoid is a matroid arising from a directed graph by the gamm…

Let $M$ be a matroid. A gammoid is a matroid arising from linkages in a directed graph; $M$ is simple if it has no loops or parallel elements, and a coline is a rank-$r(M)-2$ flat.…

Let $\mathrm{C}_A(M)$ denote the arc complexity of a gammoid $M=(E,\mathcal{I})$, where $|E|$ is its ground-set size. Unbounded arc-complexity conjecture for gammoids. For every…

Let $r,n\to\mathbb{N}$ with $n\geq r$. The uniform matroid of rank $r$ on $n$ elements is $U_{r,n}=({\{1,2,\ldots,n\}},\mathcal{I}_{r,n})$, where … Let $T=\{1,2,\ldots,r\}$,…

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…

A path-transversal system is a system arising from path transversals in a dimaze. The (I3) conjecture. Any path-transversal system satisfies (I3). The preceding discussion notes th…

Let $(D,B_0)$ be a dimaze, and let $M_L(D,B_0)$ be its linkability system. For every $I\in M_L(D,B_0)$ and every $B\subseteq B_0$, suppose there is a maximal independent set in…