h-VECTORS OF GENERALIZED ASSOCIAHEDRA AND NONCROSSING PARTITIONS

@inproceedings{Athanasiadis2008hVECTORSOG,
  title={h-VECTORS OF GENERALIZED ASSOCIAHEDRA AND NONCROSSING PARTITIONS},
  author={Christos A. Athanasiadis and Thomas Brady and Jon McCammond},
  year={2008}
}
A case-free proof is given that the entries of the h-vector of the cluster complex ∆(Φ), associated by S. Fomin and A. Zelevinsky to a finite root system Φ, count elements of the lattice L of noncrossing partitions of corresponding type by rank. Similar interpretations for the h-vector of the positive part of ∆(Φ) are provided. The proof utilizes the appearance of the complex ∆(Φ) in the context of the lattice L, in recent work of two of the authors, as well as an explicit shelling of ∆(Φ). 

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