2 problems

Let a complex of oriented matroids (COM) be a set family of VC-dimension $d$, and let an ample completion be an ample partial cube containing it. COM ample-completion conjecture. A…

Let $C$ be an extremal class. A concept $c\in C$ is a corner of $C$ if $C\setminus\{c\}$ is extremal. Corner-peeling conjecture. Every nonempty extremal class $C$ has at least one…