Enumerative properties of generalized associahedra

By Frédéric Chapoton. 2004

94 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/29fe881e84b789faee7066854df67c3d004f0aec

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In Discrete Mathematics and Combinatorics

1. David Bessis
2. B. Keller
3. Nathan Reading
4. Drew Armstrong
5. David E. Speyer
6. Michelle L. Wachs
7. S. Cecotti
8. C. Vafa

In Geometry and Topology

1. David Bessis
2. B. Keller
3. I. Reiten
4. Ralf Schiffler
5. Pierre-Guy Plamondon
6. Osamu Iyama
7. Bernard Leclerc
8. Alexander Kuznetsov

In Spectroscopy

1. David Bessis
2. B. Keller

Citations in the corpus

• Finite complex reection arrangements are K(; 1) (2015, background): “In the Weyl group case, Poin(S) may be interpreted as the Poincaré polynomial of the cohomology of a toric variety related to cluster algebras ([20]).”
• Cluster algebras and derived categories (2012, background): “] [91] ...; Cluster algebras and derived categories 3 • higher Teichmu¨ller spaces [35] [36] [37] [38] [39] ...; • combinatorics and in particular the study of polyhedra like the Stasheff associahedra [21] [22] [42] [43] [71] [90] [102] [104] [103] [130] ...; • commutative and non commutative algebra”
• Finite complex reflection arrangements are $K(\pi,1)$ (2006, unknown): “In the Coxeter case, Chapoton (see [22]) discovered a general formula for the number ZW (N) of weak chains s1 4 s2 4 · · · 4 sN−1 of length N − 1 in (S,4) or, equivalently (by Lemma B.”
• Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups (2006, unknown): “However, the only known geometric realization of ∆(W ) as a convex polytope (due to Chapoton, Fomin and Zelevinsky [43]) does not obviously extend to the noncrystallographic case, and it is an open problem to give a geometric realization of ∆(W ) when W is noncrystallographic.”
• Noncrossing partitions and the shard intersection order (2009, unknown): “The latter recursion can be solved non-uniformly [35, Theorem 3.6] to give a uniform formula first pointed out in [13, Proposition 9].”
• Triangulated Categories: Cluster algebras, quiver representations and triangulated categories (2008, unknown): “n geometry [70] [71] ..., •integrable systems [55] ..., •higher Teichmu¨ller spaces [47] [44] [45] [46] ..., •combinatorics and the study of combinatorial polyhedra like the Stasheff associahedra [34] [33] [100] [49] [109] [50] ..., •commutative and non commutative algebraic geometry, in particular t”