4 problems

Let $d6f2$ be a Coxeter diagram of type $D_n$ with $n\geq 3$. Construct the $(s_n,s_{n-1})$-subdivision $d6f2'_d6f2$ of the simplicial complex $d6f2_d6f2$ by subdividing each edge…

Let $W$ be a finite reflection group of rank $n$, let $R^{(1\mid1)}_W$ be its superspace coinvariant-type quotient, and let $\mathcal{OP}_W$ be the Coxeter complex formed by the fa…

Let $A_S$ be an irreducible spherical Artin group, let $\Delta_S$ be its associated Artin complex, and let $\mathsf C_S$ be its associated Coxeter complex with the natural action o…

Let $T$ be a tree with $n$ nodes and $b$ leaves, and let $cDelta_T$ be its Coxeter-like complex. Babson–Reiner conjecture. The complex $cDelta_T$ is at least $(n-1-b)$-connected. T…