2 problems

Genericity conjecture. For $m\geq 3$, $\mathcal{D}_n^{\operatorname{gen}(m)}$ consists exactly of the $m\times(n+1)$ $\{0,1\}$-matrices such that, for every $k\in[0,n]$, there are…

Unimodular density conjecture. The probability that a uniformly random element of $M_{n,k}({\mathbb F}_q[x];m)$ is unimodular is given by