3 problems

Ellipsoidal separation conjecture. For every fixed $\alpha\in(0,1)$, there exists a dimension $n_0(\alpha)$ such that, for all $n\ge n_0(\alpha)$, the three ellipsoids…

Permanental Sihong polynomial conjecture. The polynomial above is totally nonnegative for all $n$. This would provide a permanental analogue of the known totally nonnegative determ…

Let $A$ be a totally positive $n\times n$ matrix. For index sequences $\alpha$ and $\beta$ defining products of minors, write $\alpha/\beta$ for the corresponding ratio. A ratio is…