5 problems

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…

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

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 $[\lambda_i,\lambda_j]$…