Shellability of noncrossing partition lattices

DOI10.1090/S0002-9939-06-08534-0zbMath1171.05053arXivmath/0503007OpenAlexW2056477362MaRDI QIDQ3420072

Christos A. Athanasiadis, Thomas Brady, Colum Watt

Publication date: 1 February 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503007

zbMATH Keywords

partially ordered setshellabilitynoncrossing partitionsCoxeter elementreal reflection groupreflection ordering

Mathematics Subject Classification ID

Related Items (21)

Symmetric decompositions and the strong Sperner property for noncrossing partition lattices ⋮ The zero loci of \(F\)-triangles ⋮ On some enumerative aspects of generalized associahedra ⋮ On the homology of the noncrossing partition lattice and the Milnor fibre ⋮ Noncrossing partitions and Bruhat order ⋮ The absolute order on the hyperoctahedral group ⋮ A poset fiber theorem for doubly Cohen-Macaulay posets and its applications. ⋮ Noncrossing partitions and Milnor fibers ⋮ EL-shellability and noncrossing partitions associated with well-generated complex reflection groups ⋮ On noncrossing and nonnesting partitions of type \(D\) ⋮ Decomposition numbers for finite Coxeter groups and generalised non-crossing partitions ⋮ The absolute order on the symmetric group, constructible partially ordered sets and Cohen-Macaulay complexes ⋮ Noncrossing partitions and the shard intersection order ⋮ Clusters, Coxeter-sortable elements and noncrossing partitions ⋮ Proof of the \(K(\pi,1)\) conjecture for affine Artin groups ⋮ Shellability and higher Cohen-Macaulay connectivity of generalized cluster complexes ⋮ Connectivity properties of factorization posets in generated groups ⋮ The noncrossing bond poset of a graph ⋮ Coxeter-Catalan combinatorics and Temperley-Lieb algebras ⋮ Generalized noncrossing partitions and combinatorics of Coxeter groups ⋮ The intermediate orders of a Coxeter group

Cites Work

• Unnamed Item
• Unnamed Item
• Non-crossing partitions for classical reflection groups
• \(Y\)-systems and generalized associahedra
• Enumerative properties of generalized associahedra
• \(K(\pi,1)\)'s for Artin groups of finite type.
• ad-nilpotent ideals of a Borel subalgebra: generators and duality
• Sur les partitions non croisées d'un cycle. (The non-crossed partitions of a cycle)
• Combinatorics of Coxeter Groups
• The dual braid monoid
• Finite Reflection Groups
• B-Stable Ideals in the Nilradical of a Borel Subalgebra
• Noncrossing Partitions in Surprising Locations
• Shellable and Cohen-Macaulay Partially Ordered Sets
• Noncrossing Partitions for the GroupDn
• On a refinement of the generalized Catalan numbers for Weyl groups
• Non-crossing partition lattices in finite real reflection groups
• A partial order on the symmetric group and new \(K(\pi,1)\)'s for the braid groups

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