Colored posets and colored quasisymmetric functions

DOI10.1007/s00026-010-0059-0zbMath1231.05277arXivmath/0610984OpenAlexW2128843758MaRDI QIDQ659586

Samuel K. Hsiao, T. Kyle Petersen

Publication date: 24 January 2012

Published in: Annals of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610984

zbMATH Keywords

combinatorial Hopf algebracolored posetcolored \(P\)-partitioncolored peak algebracolored quasisymmetric function

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Combinatorics of partially ordered sets (06A07) Algebraic aspects of posets (06A11) Connections of Hopf algebras with combinatorics (16T30)

Related Items (11)

The colored Eulerian descent algebra ⋮ Specializations of colored quasisymmetric functions ⋮ The Eulerian distribution on the fixed-point free involutions of the hyperoctahedral group ⋮ A self paired Hopf algebra on double posets and a Littlewood-Richardson rule ⋮ Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras. ⋮ Shuffle-compatible permutation statistics. II: The exterior peak set ⋮ Specializations of colored quasisymmetric functions and Euler-Mahonian identities ⋮ Hopf algebra structure of generalized quasi-symmetric functions in partially commutative variables ⋮ Sign variation and descents ⋮ Sign variation and descents ⋮ Character formulas and descents for the hyperoctahedral group

Cites Work

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• Structure of the Malvenuto-Reutenauer Hopf algebra of permutations
• Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian
• Higher order peak algebras
• Enriched \(P\)-partitions and peak algebras
• A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes
• Hopf algebra of the planar binary trees
• Incidence Hopf algebras
• Shifted quasi-symmetric functions and the Hopf algebra of peak functions
• Cycle type and descent set in wreath products
• The peak algebra of the symmetric group
• Noncommutative symmetric functions
• Duality between quasi-symmetric functions and the Solomon descent algebra
• On posets and Hopf algebras
• Yang-Baxter bases of 0-Hecke algebras and representation theory of 0-Ariki-Koike-Shoji algebras.
• Coloured peak algebras and Hopf algebras.
• On the structure of Hopf algebras
• A note on three types of quasisymmetric functions
• Combinatorial Hopf algebras and generalized Dehn–Sommerville relations
• Coalgebras and Bialgebras in Combinatorics
• A generalization of solomon’s algebra for hyperoctahedral groups and other wreath products
• The peak algebra and the descent algebras of types B and D
• A Solomon descent theory for the wreath products $G\wr\mathfrak S_n$
• Enriched 𝑃-Partitions
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]

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