Enumerative properties of generalized associahedra

Abstract

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 its two spectral sequences. A precise enumerative relation with the lattices of generalized noncrossing partitions is conjectured and some evidence is given.

15 pages

Cited by in corpus (14)

• Counting factorizations of Coxeter elements into products of reflections
• Chains in the noncrossing partition lattice
• A new Garside structure for braid groups of type $(e,e,r)$
• Orbites d'Hurwitz des factorisations primitives d'un élément de Coxeter
• Non-crossing partitions of type (e,e,r)
• Counting chains in the noncrossing partition lattice via the W-Laplacian
• EL-Shellability and Noncrossing Partitions Associated with Well-Generated Complex Reflection Groups
• Hurwitz numbers for reflection groups II: Parabolic quasi-Coxeter elements
• Hochschild lattices and shuffle lattices
• Symmetric Decompositions and the Strong Sperner Property for Noncrossing Partition Lattices
• The Rank Enumeration of Certain Parabolic Non-Crossing Partitions
• Lyashko-Looijenga morphisms and primitive factorizations of the Coxeter element
• Rooted Clusters for Graph LP Algebras
• Refined Lattice Path Enumeration and Combinatorial Reciprocity