3 problems

Let $A=(a_{ij})$ be a real $n\times n$ matrix with non-negative entries, and let $J$ denote the all-ones matrix. Assume that the entries of $A$ are weakly increasing down columns.…

Let $g\geqslant 0$, $n\geqslant 1$, and let $\mu_1,\ldots,\mu_n\geqslant 1$. The deformed monotone Hurwitz number $\vec{H}^t_{g,n}(\mu_1,\ldots,\mu_n)$ is a polynomial in $t$. Two…

Interlacing conjecture. If $M$ and $M/e$ are both non-degenerate, then $Q_M(t)$ interlaces $Q_{M/e}(t)$.