4 problems

Let $I_d(d,2d-1)$ be the ideal generated by the maximal permanents of the generic $d\times(2d-1)$ matrix $M_{d,2d-1}$ over a field $k$. Monomial conjecture for maximal permanents.…

Let $M_{m,n}=(x_{i,j})$ be a generic $m\times n$ matrix over a field $k$, and let $I_d(m,n)\subset k[x_{i,j}]$ be generated by the permanents of its $d\times d$ submatrices. A mini…

Let $X$ and $Y$ be generic $n$ by $n$ matrices, let $I$ be the ideal generated by all entries of $XY-YX$, and let $J$ be generated by the off-diagonal entries. The determinants for…

Let $X$ and $Y$ be generic $n$ by $n$ matrices, let $J$ be the ideal generated by the off-diagonal entries of $XY-YX$, and consider determinants of matrices whose columns are the d…