The minor ideal generation conjecture for the matrix A

Let $r$ be the number of variables, set $t_2=r(r-1)/2$, and let $M(d,\ell)$ be the set of $(\tau,\nu)$-monomials of degree $d$ whose $\nu$-part is admissible and contains at least $\ell$ distinct $\nu_i$. For $e\geq 0$, let $\operatorname{Min}_e(A)$ denote the $e$-th minor ideal of the matrix $A$.

Minor ideal generation conjecture. For all $e\geq 0$, the ideal $\operatorname{Min}_e(A)$ is generated by $M(e,r-1-t_2+e)$.

This conjecture refines the previously known description of minor ideals for $\tilde M_r$ and gives a proposed explicit generating set for the minor ideals of $A$. The source provides no resolution status.