8 problems

For positive integers $m$ and $n$, let $L(m,n)$ be the poset of $m$-tuples … ordered coordinatewise, with rank $\sum_{r=1}^m a_r$. A chain is saturated if it skips no rank, and sym…

Let $\mathcal P$ be the set of partitions, and consider Young's lattice with a constant symbol for every partition, $\left\langle \mathcal P,\leq,\pi:\pi\in\mathcal P\right\rangle$…

Let $\textbf{Y}=\left\langle \mathcal P,\leq\right\rangle$ be Young's lattice, where $\mathcal P$ is the set of partitions ordered by inclusion of their Young diagrams. The Sigma-1…

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

The map $k\frac{\partial}{\partial p_k}p_k$ acts on homogeneous symmetric functions of degree $n$. With respect to an integral basis, let $M_k^{(n)}$ denote its matrix, and let…

Let $T_1,T_2,\dots,T_k$ be a $K$-Knuth class of straight tableaux, and let $T_i$ have shape $\lambda_i$. Write … Order Young diagrams by inclusion, and let $[\lambda_i,\lambda_j]$…