3 problems

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…

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

Let $\Delta_k(n)$ be the broken $k$-diamond partition function, and set $a_n=\Delta_k(n)$. Define … … and $I=A^3-27B^2$. Invariant positivity conjecture. For $k=1$ or $2$ and…