4 problems

Let $M$ be a matroid, and call a rank-$k$ flat ordinary if it is the direct sum of a point and a rank-$(k-1)$ flat. Ordinary-flat conjecture. For each integer $k\ge 2$, every compl…

Normalized average flat-size conjecture. This average is at most $1+o_n(1)$. The source presents this as a strengthening of the preceding asymptotic flat-size conjecture; the meani…

Let $M$ be a simple $n$-element, rank-$r$ complex-representable matroid, where $r\fixed$ and $r73$. The average flat-size is the average of $|F|$ over the flats $F$ of $M$. Average…

Let $M$ be a simple $n$-element, rank-$4$, complex-representable matroid that is not the union of two lines. Its average plane-size is the average of $|P|$ over the rank-$3$ flats…