10 problems

Geometric Jordan-type conjecture. For all $i,j\in\mathbb{Z}$, the partitions in the growth diagram of $w$ should be interpretable as the Jordan types of

Geometric realization conjecture. The growth diagrams constructed in the paper should admit a natural geometric realization in terms of relative positions of affine flags, analogou…

Almost Pieri coloring conjecture. There exists an admissible $\widetilde{Q}\in\operatorname{SYT}(\lambda)$ such that $\widetilde{Q}^\uparrow$ admits a $\widetilde{\alpha}$-coloring…

Almost Pieri rule.

Strict-partition coloring conjecture. For each $\lambda\in\mathcal{S}_\alpha$, there exists an admissible $Q\in\operatorname{SYT}(\lambda)$ such that $Q^\uparrow$ admits an…

Strict-partition conjecture. begin{enumerate} item If $\nu_s>1$, then $\mathcal{S}_\nu=\mathcal{B}_\nu$. item If $\nu_s=1$ and $m$ is odd, then $\mathcal{S}_\nu=\mathcal{B}_\nu$. i…

Let $(\tau_n)_n$ be a sequence of conjugation-invariant random permutations, and let $\mathrm{LDS}_k(\tau_n)$ denote the maximum total length of $k$ decreasing subsequences of…

Injectivity conjecture. Then

Let $G(r,n)$ be the wreath product reflection group, and let $(i_1,\ldots,i_r;j_1,\ldots,j_r)$ be a $2r$-tuple of nonnegative integers satisfying … Consider the submodule spanned b…

Mirabolic RSK cell conjecture. Two colored permutations $\tilde w,\tilde w'\in RB_N$ lie in the same bimodule Kazhdan–Lusztig cell if and only if