2 problems

Let $Q$ be a word in the simple generators of a finite Coxeter group, let $\omega$ be a Coxeter-group element, and let $[e,\omega]$ be the corresponding interval in the weak order.…

Let $Q$ be a sorting and alternating word in a Coxeter group with longest element $\omega_\circ$, let $\mathsf{Brick}(Q,\omega_\circ)$ be the associated brick polytope, and let…