2 problems

Determinantal threshold conjecture. For $k=1$ or $2$ and $1\leq m\leq14$, one has

Laguerre threshold conjecture. For $k=1$ or $2$ and $1\leq m\leq14$, the sequence $\Delta_k(n)$ satisfies the Laguerre inequality of order $m$, namely $L_m(\Delta_k(n))\geq0$, for…