3 problems

Let $W$ be a finite Weyl group with positive-root poset $\Phi^+$, rank $r$, Coxeter number $h$, and longest element $w_0\in W$. Let $\operatorname{NN}(W)=\mathcal{A}(\Phi^+)$ be th…

Let $W$ be a finite Weyl group with root system $\Phi$, positive roots $\Phi^+$, rank $r$, Coxeter number $h$, and simple roots $\\{\alpha_1,\ldots,\alpha_r\\}$. Write…

Let $W$ be a finite Weyl group of rank $r$, with $h$ its Coxeter number, and let ${\sf Pan}$ be the Panyushev complement on antichains in the associated positive-root poset…