# On some enumerative aspects of generalized associahedra

@article{Athanasiadis2007OnSE,
title={On some enumerative aspects of generalized associahedra},
journal={Eur. J. Comb.},
year={2007},
volume={28},
pages={1208-1215}
}
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## References

SHOWING 1-10 OF 25 REFERENCES
Enumerative properties of generalized associahedra
Some enumerative aspects of the fans, called generalized associahedra, introduced by S. Fomin and A. Zelevinsky in their theory of cluster algebras are considered, in relation with a bicomplex and
Shellability of noncrossing partition lattices
• Mathematics
• 2005
We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type D n
Polytopal Realizations of Generalized Associahedra
• Mathematics
• 2002
Abstract We prove polytopality of the generalized associahedra introduced in [5].
K(π, 1) for Artin Groups of Finite Type
• Mathematics
• 2002
We construct K(π 1)'s for Artin groups of type C n and D n , using the lattice of elements preceding a Coxeter element in the partial order defined by reflection length.
K(π 1)'s for Artin Groups of Finite Type
• Mathematics
• 2000
We construct K(π 1)'s for Artin groups of type Cn and Dn, using the lattice of elements preceding a Coxeter element in the partial order defined by reflection length.
Generalized cluster complexes and Coxeter combinatorics
• Mathematics
• 2005
We introduce and study a family of simplicial complexes associated to an arbitrary finite root system and a nonnegative integer parameter m. For m=1, our construction specializes to the (simplicial)
Lattices in finite real reflection groups
• Mathematics
• 2005
For a finite real reflection group $W$ with Coxeter element $\gamma$ we give a uniform proof that the closed interval, $[I, \gamma]$ forms a lattice in the partial order on $W$ induced by reflection
Y-systems and generalized associahedra
• Mathematics
• 2003
The goals of this paper are two-fold. First, we prove, for an arbitrary finite root system D, the periodicity conjecture of Al. B. Zamolodchikov [24] that concerns Y-systems, a particular class of
Cluster algebras II: Finite type classification
• Mathematics
• 2002
This paper continues the study of cluster algebras initiated in math.RT/0104151. Its main result is the complete classification of the cluster algebras of finite type, i.e., those with finitely many