3 problems

Problem. Is every finite uniformly dense matroid of rank $3$ cyclically orderable?

Let $M=(S,\mathcal{B})$ be a matroid with rank function $r_M$. It is uniformly dense if … for every $X\subseteq S$. A matroid is cyclically orderable if its ground set has a cyclic…

Exponential density conjecture. If $M=(E,G)$ is a full-rank, $r$-dimensional matroid with no induced $I_t$-restriction, then