4 problems

Inverse Grassmannian descent-removal conjecture. Suppose $u,v\in S_\infty$ are inverse Grassmannian with unique left descents $i$ and $j$, respectively. Then, for every…

Multiplicity-free inverse Grassmannian conjecture. If $u$ and $v$ are inverse Grassmannian, then $\mathfrak S_u\cdot\mathfrak S_v$ is a multiplicity-free sum of Schubert polynomial…

Inverse Grassmannian coefficient conjecture. If $u$ and $v$ are inverse Grassmannian, then

Let $\alpha\in\overline{\sf KM}_n$ and let $\beta\in\sf Qlswap(\alpha)$. The quasi-key polynomial $\mathfrak D_\beta$ is multiplicity-free when all entries of $\alpha$ are positive…