Mason's rank conjecture for symmetric powers of matroids

Let $M$ be a matroid, let $V$ be the ambient vector space used to define its symmetric quasi-powers, and let $N$ be a $k$-th symmetric quasi-power of $M$. Write $N_k$ for the relevant matroid on the $k$-th symmetric power and, for a flat $F$ of $M$, write $F\cdot {\rm Sym}_{k-1}(V)$ for the corresponding subset of the ground set of $N_k$.

Mason's rank conjecture. The rank of $N$ is

$$\binom{\operatorname{rank} M +1}{k}$$

if and only if $F\cdot {\rm Sym}_{k-1}(V)$ is a flat of $N_k$ for every flat $F$ of $M$.

This conjecture formalizes Mason's proposed implication that the SP-rank property should follow from the symmetric quasi-power and flat properties. The source identifies it as an outstanding open question, later stated formally by Anderson.