6 problems

Robichaux's ghost Kohnert conjecture. For every permutation $w\in S_n$ and $\alpha\in\mathbb{Z}_{\geq 0}^n$,

Ross–Yong's Grothendieck-polynomial conjecture. For every permutation $w\in S_n$,

Robichaux's support conjecture. Robichaux's rule correctly computes the support of Grothendieck polynomials: for every permutation $w\in S_n$,

Ross–Yong's conjecture. Their rule provided a combinatorial model for both Grothendieck polynomials and Lascoux polynomials, the $K$-theoretic Demazure characters.

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 $\chi_{D_{\mathrm{top}}(w)}$.