On the Sperner property for the absolute order on complex reflection groups

DOI10.5802/alco.114OpenAlexW2921670843MaRDI QIDQ2187948

Yibo Gao, Christian Gaetz

Publication date: 3 June 2020

Published in: Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.02033

zbMATH Keywords

antichainreflection groupSperner propertyabsolute ordernormalized flow

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Algebraic aspects of posets (06A11)

Related Items (3)

The hull metric on Coxeter groups ⋮ The absolute orders on the Coxeter groups \(A_n\) and \(B_n\) are Sperner ⋮ The intermediate orders of a Coxeter group

Uses Software

• SageMath

Cites Work

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• The morphology of partially ordered sets
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• Symmetric decompositions and the strong Sperner property for noncrossing partition lattices
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• Comparing Codimension and Absolute Length in Complex Reflection Groups
• Generalized noncrossing partitions and combinatorics of Coxeter groups
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property
• The symmetric group, ordered by refinement of cycles, is strongly Sperner
• A combinatorial 𝔰𝔩₂-action and the Sperner property for the weak order
• Absolute order in general linear groups
• Invariants of Finite Reflection Groups
• Finite Unitary Reflection Groups

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