5 problems

Simultaneous reflection-length reduction conjecture. There exists a letter $s$ in $u_1\cdots u_p$ such that, after omitting it,

Reflection-length upper-bound conjecture. The upper bounds from the results for $n=3$ and $n\geq 4$ are equal to the reflection length function itself.

Deletion-set containment conjecture. There always exists a deletion set $D(\mathbf{s})$ for $W$ such that $D(\mathbf{s})$ is contained in a deletion set of $\mathbf{s}$ in the univ…

Let $W$ be a Coxeter group, and let $\ell_R$ denote its reflection length function. The group $W$ is of spherical type if it is finite, and of affine type if it is an affine Coxete…

Let $W$ be an affine Coxeter group, let $w=t_\lambda w_0$ with $w_0\in W_0$ fixing the origin, and let $\lambda$ be $k$-dimensional. Here $\ell_R$ denotes reflection length. Additi…