3 problems

Let $\mathfrak{S}_n$ be the symmetric group of permutations of $[n]$, and let $r\geq 1$. The statistics $r\mathsf{des}$, $r\mathsf{maj}$, $r\mathsf{exc}$, $r\mathsf{den}$,…

Let ${\cal OP}_n^k$ be the set of ordered $k$-partitions of $[n]$, and let $\mathop{\rm bmaj}$ and $\mathop{\rm binv}$ be the block-major index and block-inversion statistics. Let…

Let $\mathfrak{S}_M$ be the set of multipermutations of the multiset $M$, and let $r\geq 1$. Let $\mathsf{des}_r$, $\mathsf{maj}_r$, $\mathsf{exc}_r$, and $\mathsf{den}_r$ be the c…