The absolute orders on the Coxeter groups \(A_n\) and \(B_n\) are Sperner

DOI10.37236/8874zbMath1444.05150arXiv1902.08334OpenAlexW3046027510MaRDI QIDQ783067

Neal Livesay, Gene B. Kim, Lawrence H. Harper

Publication date: 30 July 2020

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.08334

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Extremal set theory (05D05) Ordered groups (06F15) Ordered groups (group-theoretic aspects) (20F60) Combinatorial aspects of groups and algebras (05E16)

Related Items (2)

On the Sperner property for the absolute order on complex reflection groups ⋮ The symmetric group, ordered by refinement of cycles, is strongly Sperner

Cites Work

• The absolute order on the hyperoctahedral group
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• The global theory of flows in networks
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• The weak Bruhat order on the symmetric group is Sperner
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• Generalized noncrossing partitions and combinatorics of Coxeter groups
• Morphisms for the strong Sperner property of Stanley and Griggs
• Representations of $\mathfrak{sl}( 2,\mathbb{C} )$ on Posets and the Sperner Property
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property

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