4 problems

Reflection deletion conjecture. If

Root-order conjecture. If $\check\alpha\in\check R^+(w)$ is decomposable, then there exists a decomposition

Expression-graph conjecture. For every $w\in W$, the theorem of Bergeron, Ceballos and Labbé concerning cycles in $\mathcal{R}(w)$ remains valid when $\mathcal{R}(w)$ is replaced b…

Let $w_0$ be the longest element of the relevant Weyl group, let $[\widetilde{w}_0]$ denote a commutation equivalence class of reduced expressions of $w_0$, and let an $r$-cluster…