12 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…

Let $P$ and $Q$ range over the relevant shifted standard tableaux, and let $A_{P,Q}$ denote the corresponding entry of the matrix associated with modified jeu de taquin. Symmetry c…

Let $\mathcal{P}$ be a $d$-complete poset with bottom tree $\mathcal{B}$. Let $T$ be a skew increasing $\mathcal{P}$-tableau, and let $R$ and $S$ be rectifications of $T$. Bottom-t…

Let $\mathcal{P}$ be a $d$-complete poset and let $\lambda \subseteq \mathcal{P}$ be an order ideal. A rectification target is an increasing $\mathcal{P}$-tableau obtained as the r…

Let $T$ be any (semi)standard skew tableau and let $mathbox$ be an inner co-corner of $T$. Local evacuation-shuffle algorithm conjecture. There exists a local algorithm for computi…

Let $T$ be any (semi)standard skew tableau and let $\scalebox{.5}{\young(x)}$ be an inner co-corner of $T$. Write $\operatorname{esh}$ for evacuation-shuffling,…

Let $\mathcal{O} \subseteq \mathrm{LR}(\alpha,\scalebox{.5}{\yng(1)},\beta, \gamma)$ be an orbit of $\omega$. Let $K_1(\mathcal{O})$ and $K_2(\mathcal{O})$ denote the sets of genom…

Let $\lambda$ and $\mu$ be partitions with $\lambda\vdash n$, and suppose that $\mu$ is a hook. Write $f^{\lambda/\mu}$ for the number of standard Young tableaux of skew shape…

Let $\lambda,\mu,\nu$ be partitions indexing equivariant $K$-theory Schubert classes, and let ${\tt EqINC}(\nu/\lambda,|\mu|)$ denote the relevant set of equivariant increasing tab…

Let $v$ be a permutation and fix $k$. A mixed Bruhat chain from the identity to $v$ is a concatenation of maximal chains in possibly different $l$-Bruhat orders. Such a chain has p…

The d-complete poset rectification problem. For which classes of tableaux ${\mathcal C}=\{C_\mu\}$ is it true that, if $K{\tt rect}(T)=C\in{\mathcal C}$ under one rectification ord…

Thomas–Yong's conjecture. For any minuscule $G/P$,