2 problems

Let $\mathcal D$ be a dimatroid, meaning the intersection of two matroids on a common ground set, and let $C,D\in\mathcal D$. Balancing conjecture. There exist $C',D'\in\mathcal D$…

Let $\mathcal P$ and $\mathcal Q$ be matroids on the same ground set $V$, let $\mathcal D=\mathcal P\cap\mathcal Q$, and set … A set $S$ represents a part $A$ almost $\alpha$-fairl…