Simplicial Complexes of Antichains in Root Posets and Related Combinatorics of Dyck Paths

Lili Mu, Volkmar Welker

For a crystallographic root system $\mathfrak{D}$ we consider the simplicial complex ${\Delta }_{\mathfrak{D}}$ of all antichains in the root poset of $\mathfrak{D}$. We show that $Δ_{\ma…