6 problems

Let $\mathcal{P}$ be a $d$-complete poset with bottom tree $\mathcal{B}$. Let $T$ be a skew increasing $\mathcal{P}$-tableau, and let $R$ and $S$ be rectifications of $T$. Bottom-t…

Let $X=G/P$ be a Kac–Moody flag variety, let $m \in W^P$ be $\Lambda$-minuscule, and let $\mathcal{P}_m$ be the associated $d$-complete poset. For $u,v,w \leq m$ in Bruhat order, l…

Let $\mathcal{P}$ be a $d$-complete poset and let $\lambda \subseteq \mathcal{P}$ be an order ideal. A rectification target is an increasing $\mathcal{P}$-tableau obtained as the r…

A locally finite poset is a poset in which every interval is finite. The preceding finite-poset theorem has several parts whose conclusions depend on finiteness. Infinite-counterex…

A finite poset is D3-minus-C if it satisfies the D3-minus-C axiom, and it has Short intervals are Small when that property holds. Finite D3-minus-C conjecture. If a finite poset is…

The d-complete poset hook-length bijection conjecture. If $G\in\mathcal{G}_c^0$, then $s(G)=c$ and $e(G)=G$; if $G\in\mathcal{G}_c^k$ for $k\geq1$, then…