8 problems

Let $M$ range over matroids on an $n$-element ground set, with $n$ tending to infinity. A paving matroid is a matroid whose circuits have size $r$ or $r+1$, where $r$ is its rank;…

Asymptotic paving matroid conjecture. Asymptotically almost all matroids are paving.

Paving matroid enumeration conjecture. Almost all matroids are conjectured to be paving.

Kajitani–Miyano–Ueno conjecture. The matroid $M$ is cyclically orderable if and only if

A $k$-matroid $(V,\mathcal{H})$ is a matroid whose bases are the members of the nonempty family $\mathcal{H}$, all of size $k$, satisfying the basis exchange axiom. It is conjectur…

Let $m_n$ be the number of matroids on an $n$-element ground set, and let $p_n$ be the number of those matroids that are paving. Paving matroid asymptotic conjecture. The asymptoti…

A paving matroid is a rank-$d$ matroid whose circuits have either $d$ or $d+1$ elements. The asymptotic paving matroid conjecture. Asymptotically almost all matroids are paving mat…

A paving matroid is a matroid whose circuits all have size at least its rank. For a sequence of finite matroids, say a property holds asymptotically almost every matroid when the p…