7 problems

Reiner–Tenner–Yong's conjecture. The distributive lattice $J(T_{k,n})$ is CDE.

A minuscule poset is a poset arising in the representation theory of a semisimple Lie algebra; for a poset $P$, let $J(P)$ denote its associated distributive lattice. The property…

For $n\geq1$ and $0\leq k<n/2$, let … The notation $[\varnothing,\lambda]_{\mathrm{shift}}$ denotes the corresponding initial interval in the shifted Young's lattice,…

Let $\delta_r=(r,r-1,\ldots,1)$, and for partitions let $\nu+\lambda$ denote the partition obtained by adding corresponding parts. For $a,m,n\geq 1$ with $n>am$, set … Here…

Two-staircase conjecture. The interval $[\varnothing,\lambda]_{\operatorname{shifted}}$ is CDE, with

Falling-by-twos conjecture. The interval $[\varnothing,\lambda]_{\operatorname{shifted}}$ is CDE, and

Rectangular staircase vexillary conjecture. The conclusion of Theorem applies: the posets $[varnothing,bb]$ and $[e,w]$, and their duals, are all CDE, with