2 problems

Conjecture. There exist an absolute constant $c\ge 1$ and an online algorithm such that, for every finite matroid $M$ and every choice of nonnegative weights, the algorithm selects…

A rank-$r$ matroid is paving if all its circuits have cardinality at least $r$. For each positive integer $n$, consider matroids on an $n$-element ground set. The paving matroid co…