Bijections between noncrossing and nonnesting partitions for classical reflection groups

DOI10.4171/PM/1869zbMath1203.05160arXiv0810.2613WikidataQ57441883 ScholiaQ57441883MaRDI QIDQ604625

Alex Fink, Benjamin Iriarte Giraldo

Publication date: 12 November 2010

Published in: Portugaliae Mathematica. Nova Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.2613

zbMATH Keywords

Catalan numberWeyl groupCoxeter groupnoncrossing partitionsreflection groupnonnesting partitions

Mathematics Subject Classification ID

Partitions of sets (05A18) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items

New interpretations for noncrossing partitions of classical types ⋮ Labeling the regions of the type \(C_n\) Shi arrangement ⋮ Folded bump diagrams for partitions of classical types ⋮ On noncrossing and nonnesting partitions of type \(D\) ⋮ Gray codes and lexicographical combinatorial generation for nonnesting and sparse nonnesting set partitions

Cites Work

• On noncrossing and nonnesting partitions of type \(D\)
• On noncrossing and nonnesting partitions for classical reflection groups
• Non-crossing partitions for classical reflection groups
• Deformations of Coxeter hyperplane arrangements
• \(K(\pi,1)\)'s for Artin groups of finite type.
• Sur les partitions non croisées d'un cycle. (The non-crossed partitions of a cycle)
• Combinatorics of Coxeter Groups
• The dual braid monoid
• B-Stable Ideals in the Nilradical of a Borel Subalgebra
• Decomposition numbers for finite Coxeter groups and generalised non-crossing partitions
• Generalized noncrossing partitions and combinatorics of Coxeter groups
• Noncrossing Partitions for the GroupDn
• A bijection between noncrossing and nonnesting partitions of types A and B
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