4 problems

Let $T$ be an admissible skew tableau. At each step, choose an inside corner and apply the symplectic jeu de taquin sliding procedure, iterating until a symplectic tableau is obtai…

A word $u$ has maximum letter $m$ and is $m$-packed if it contains at least one copy of every integer in $[m]=\{1,\ldots,m\}$. A word $u$ is $m$-stable when its centralizers satisf…

Strengthened row-maximum conjecture. For every $i$ with $1\leq i\leq \ell$,

Ring-generation conjecture. $\mathcal{P}_{\lambda/\mu}$ belongs to the ring generated by the shifted plactic Schur $P$-functions.