2 problems

Let $w\in \widetilde{\mathfrak{S}}_n$, let $\mathcal{C}_w(n,k)$ denote the relevant collection of consistent subsets, and let $R\in \mathcal{C}_w(n,k)$. Define $G_R$ by including e…

For an affine permutation $w\in \widetilde{\mathfrak{S}}_n$, let $\mathcal{G}(w)$ be the directed graph whose vertices are commutation classes of reduced words for $w$, with edges…