5 problems

Non-commutativity and linguization of Oshida-Rule. It is not possible to prove from the supplied formulation that this identity holds using matrices $A$; equivalently, it is not po…

Let $m$ be a positive integer, let $e$ denote the distinguished initial vector, and let $h$, $h'$, $f_1$, and $H_{245}=L\circ S$ be the maps defined above, with…

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…

Integer-image extension conjecture. The method for solving Problem 6 for $m=3$ and column typical matrices can be extended to general matrices and any $m$; in particular, one shoul…