2 problems

For a matroid $M$, let $d(M)$ be its density, and call $M$ density-critical when every proper minor $N$ satisfies $d(N)<d(M)$. Finiteness conjecture. For every $t\geq 0$, there are…

For a matroid $M$, let $\d(M)$ denote its density, and call $M$ strictly $t$-density-critical when $d(M)>t$ while every proper minor $N$ of $M$ satisfies $d(N)\leq t$. Finiteness c…