5 problems

Submodular-cut extension conjecture. There exists an extension $\mathcal{O}\cup p'$ corresponding to $\mathcal{M}'$.

Mandel's conjecture. Every oriented matroid $\mathcal{O}$ has an extension $g$ in general position (not a coloop) such that $(\mathcal{O}\cup g,g,f)$ is a Euclidean oriented matroi…

A matroid is hypermodular if every pair of two distinct maximal proper flats is modular. A matroid is a restriction of another matroid if it is obtained by restricting that matroid…

Let $M$ be a matroid. It is sticky if, for any two matroids $N_1$ and $N_2$ with $E(M)=E(N_1)\cap E(N_2)$ and $M=N_1|_{E(M)}=N_2|_{E(M)}$, there exists an amalgam of $N_1$ and…

Let $M$ be a matroid. A modular cut is a set of flats closed upward and closed under intersections of modular pairs; $M$ is OTE (only trivially extendable) if every modular cut oth…