4 problems

Let $\b5$ be a partition of $n$, let $\bf M_{\b5}$ be its lattice diagram module, and let $\bf B_{ij}$ be the modules assigned recursively to the cells $(i,j)$ of $\b5$. Bergeron–H…

Let $\bd_1,\bd_2,\ldots,\bd_d$ be the lattice diagram modules associated with the partitions obtained by removing the corner cells of a partition. Science Fiction conjecture. The m…

Let $\b5$ be a partition of $n+1$, let $(i,j)$ be a cell of $\b5$, and let the shadow of $(i,j)$ be the set of cells $(i',j')$ in $\b5$ satisfying $i\leq i'$ and $j\leq j'$. Let…

Let $\bf M_{\b5/ij}$ be the bigraded $S_n$-module formed by the partial derivatives of the lattice diagram alternant associated with the diagram obtained from a partition $\b5$ of…