4 problems

Let $\Lambda^p$ be the module indexed by a partition $p$ of $n$. Write $\mathsf{Rad}^{(j)}_{\mathcal{P}_n}\Lambda^p$ and $\mathsf{Rad}^{(j)}_{\mathcal{D}_n}\Lambda^p$ for the $j$th…

Let $n$ be odd, let $\tilde{d4ad4e}_n$ be the left ideal described in the preceding corollary, and let $\tilde{M}_i$ denote its elements indexed by $0d4a i\frac{n-1}{2}$. Dimension…

Non-negativity conjecture. The coefficients

Let $\mathscr{P}\mathscr{C}$ denote the set of peak compositions. For each $\alpha\in\mathscr{P}\mathscr{C}$, let $\Pi_\alpha$ be the peak-algebra basis element, let…