6 problems

Let $W$ be a finite reflection group containing $-1$, let $G$ be its Dynkin diagram, and let $\bar G$ be an orientation. Form the Coxeter element $c$ from the oriented diagram, ord…

Let $W$ be a finite reflection group containing $-1$, let $G$ be its Dynkin diagram, and let $\bar G$ be an orientation. Order the roots using their order as inversions in the word…

Let $G$ be a finite reflection group acting on $\mathbb{R}^k$, let $P(s)$ be the product of the distances from $s=(s_1,\ldots,s_k)$ to all reflecting hyperplanes of $G$, and let…

Helly property conjecture. If $k\geq 3$ and $w_1W_{\pi_1},\dots,w_kW_{\pi_k}\in\operatorname{PF}$ satisfy

Let $W$ be a well-generated reflection group acting on a complex vector space $V$. A frame $\Lambda$ is the auxiliary structure used to define the properties strongly stratified an…

Let $W$ be a well-generated reflection group acting on a complex vector space $V$. A generating set $R$ is well-generating when it generates $W$ and has cardinality $\dim V$. The s…