Polygon dissections and some generalizations of cluster complexes

Let $W$ be a Weyl group corresponding to the root system $A_{n-1}$ or $B_n$. We define a simplicial complex $\Delta^m_W$ in terms of polygon dissections for such a group and any positive integer $m$. For $m=1$, $\Delta^m_W$ is isomorphic to the cluster complex corresponding to $W$, defined in \cite{FZ}. We enumerate the faces of $\Delta^m_W$ and show that the entries of its $h$-vector are given by the generalized Narayana numbers $N^m_W(i)$, defined in \cite{Atha3}. We also prove that for any $m \geq 1$ the complex $\Delta^m_W$ is shellable and hence Cohen-Macaulay.