4 problems

Orthogonal Sagan–Worley insertion conjecture. For every $i\in\mathbb{Z}$,

Partition-folding bijection conjecture. There exists a bijection $\varphi$ on permutations that preserves the inverse descent set such that, if $u$ and $v$ are $\mu$-equivalent, th…

Generalized dual equivalence conjecture. For a partition $\mu$, the quasisymmetric generating function of each generalized dual equivalence class under $D_i^{\mu}$ is symmetric and…

A shifted dual equivalence is a family of involutions satisfying the stated local axioms for shifted tableaux and peak sets. The paper considers weak dual equivalence as the analog…