5 problems

For each $n$, let $\mathrm{PF}_{n}$ be the proportion of distinct first-row Kazhdan–Lusztig polynomials for $\mathrm{S}_{n}$ having the Perron–Frobenius property, and let…

Let $A$ and $B$ be matrices, let $\sigma_{(max+)}(A)$ and $\sigma_{(max+)}(B)$ denote their max-plus eigenspaces, and let $\mathscr{P}_{\infty}(A)$ and $\mathscr{P}_{\infty}(B)$ de…

Critical-eigenvector conjecture. If, for every other $w=(0,w_1,w_2)\in\sigma_{max+}(A)$, there exists an $\alpha>0$ with $\alpha\in\mathbb{R}$ such that $v_1=w_1+\alpha$ and…

Let $\Gamma$ be a strongly connected graph. Its Perron–Frobenius eigenspace is the eigenspace corresponding to the Perron–Frobenius eigenvalue of its vertex matrix. Quantum vertex-…

Let $CE_n$ denote the critical exponent for $n$-by-$n$ generalized doubly nonnegative matrices, and let $MIP_n$ be the maximum index of primitivity among primitive $n$-by-$n$ gener…