Polygon dissections and some generalizations of cluster complexes |
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Authors: | Eleni Tzanaki |
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Institution: | Department of Mathematics, University of Crete, 71409 Heraklion, Crete, Greece |
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Abstract: | Let W be a Weyl group corresponding to the root system An−1 or Bn. We define a simplicial complex in terms of polygon dissections for such a group and any positive integer m. For m=1, is isomorphic to the cluster complex corresponding to W, defined in S. Fomin, A.V. Zelevinsky, Y-systems and generalized associahedra, Ann. of Math. 158 (2003) 977-1018]. We enumerate the faces of and show that the entries of its h-vector are given by the generalized Narayana numbers , defined in C.A. Athanasiadis, On a refinement of the generalized Catalan numbers for Weyl groups, Trans. Amer. Math. Soc. 357 (2005) 179-196]. We also prove that for any m?1 the complex is shellable and hence Cohen-Macaulay. |
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Keywords: | Generalized cluster complex Generalized associahedron Generalized Narayana numbers |
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