Abstract

Abstract. Let W be a Weyl group corresponding to the root system An−1 or Bn. We define a simplicial complex ∆m W in terms of polygon dissections for such a group and any positive integer m. For m = 1, ∆m W is isomorphic to the cluster complex corresponding to W, defined in [8]. We enumerate the faces of ∆m W and show that the entries of its h-vector are given by the generalized Narayana numbers Nm W (i), defined in [3]. We also prove that for any m≥1 the complex ∆m W is shellable and hence Cohen-Macaulay. 1. Introduction and

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