5 problems

Let $u,v\in S_n$ be vexillary permutations, let $\phi(w)$ be the Wachs flag of $w$, and write $a\preceq b$ when $a$ is a prefix of $b$. Let $\mathfrak G_w^{(\beta)}(\mathbf x)$ be…

Let $u,v\in S_n$ be vexillary permutations, let $\phi(w)$ be the Wachs flag of $w$, and write $a\preceq b$ when $a$ is a prefix of $b$. Let $\mathfrak S_w(\mathbf x;\mathbf y)$ be…

Almost vexillary support conjecture. For every almost vexillary permutation $w$, there exists a subset $A\subset D(w)$ such that

Hafner–Mészáros–Setiabrata–St. Dizier conjecture. For any vexillary permutation $w$, $\hat{\mathfrak{G}}_w$ equals an integer multiple of $\chi_{D_{\mathrm{top}}(w)}$.

Let $\omega$ be a partial permutation, and let $X_\omega\subset\mathfrak{M}_{m,n}(\mathbb{R})$ denote the corresponding open dense regular part of the real matrix Schubert variety.…