4 problems

Reflection deletion conjecture. If

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

Let $W$ be a Coxeter group with reflection set $T$, and let ${\mathrm{Red}_T}(w)$ denote the set of minimal-length expressions of $w$ as a product of reflections. Suppose that … an…

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…