3 problems

Let $d$ and $n$ be positive integers, and let $\mathcal{R}_{d}(\mathfrak{S}_{n})$ denote the set of permutations $\pi\in\mathfrak{S}_{n}$ satisfying $\pi^d=e$, equivalently, the pe…

Let $\operatorname{cdes}_m$ denote the cyclic descent statistic on permutations of size $m$, and let a permutation statistic be symmetric if it is realizable as the symmetric exten…

Cyclic descent map conjecture. Every skew shape, with the exception of connected ribbons, has a cyclic descent map.