Polygon Dissections and Some Generalizations of Cluster Complexes for the Classical Reflection Groups

@inproceedings{Tzanaki2005PolygonDA,
  title={Polygon Dissections and Some Generalizations of Cluster Complexes for the Classical Reflection Groups},
  author={Eleni Tzanaki},
  year={2005}
}
We define a simplicial complex ∆ W in terms of polygon dissections for every classical reflection group W and positive integer m. For m = 1, ∆ W is isomorphic to the cluster complex corresponding to W , defined in [8]. We enumerate the faces of ∆ W and show that the entries of its h-vector are given by the generalized Narayana numbers N W (i), defined in [3]. We also prove that for any m ≥ 1 the complex ∆ W is shellable and hence Cohen-Macaulay.