4 problems

Let $S\in\binom{[n]}{k}$ and let $\lambda$ be a partition inside $R(n,k)$. Write $S(\lambda)$ for the collection of $k$-subsets defined by the containment conditions in the paper,…

Let $\mu$ be a partition with $n$ removable corners $\{c_1,\dots,c_n\}$, let $1\leq k\leq n-1$, and let $\lambda$ be a partition inside the rectangle $R_{n,k}=((n-k)^k)$. For…

For a partition $\mu\vdash n$, let $\mathcal{H}_\mu$ be the doubly graded Garsia–Haiman module, and let its Frobenius series encode the doubly graded $\mathfrak{S}_n$-module struct…

Let $\lambda$ be an integer partition of $n+1$, and let $\mu^{(1)},\ldots,\mu^{(k)}$ be partitions of $n$, each obtained from $\lambda$ by removing a removable cell from its Young…