10 problems

Let Schubert polynomials be the polynomial family associated with permutations. Kohnert conjectured that each Schubert polynomial admits a generating-polynomial interpretation in t…

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.

Let $w\in S_n$ and $\gamma\in\mathbb{Z}_{\geq 0}^n$. Let $\overline{{\sf KKoh}}(w,\gamma)$ denote the modified family of diagrams associated with $w$ and weight $\gamma$, and let…

Let $w\in S_n$ and $\gamma\in\mathbb{Z}_{\geq 0}^n$. Write $g_{w,\gamma}=\#\{P\in {\sf Pipes}(w)\mid {\tt wt}(P)=\gamma\}$, and let ${{\sf KKoh}}(w,\gamma)$ be the set of diagrams…

Finite forbidden-subdiagram conjecture. There exists a finite number of special families of subdiagrams $\mathcal{F}$ such that, for any diagram $D_0$, $\mathcal{P}(D_0)$ is ranked…

Flagged Schur module character conjecture. For every northwest diagram $D$,

Let $a=(a_1,otsc,a_n)in\boldsymbol{Z}_{geq0}^n$. A K-Kohnert diagram is a subset $D$ of $\boldsymbol{Z}_{>0}^n$ together with a subset of marked boxes, obtained from the skyline di…