THE HOPF ALGEBRAS OF SYMMETRIC FUNCTIONS AND QUASI-SYMMETRIC FUNCTIONS IN NON-COMMUTATIVE VARIABLES ARE FREE AND CO-FREE

DOI10.1142/S0219498809003485zbMath1188.16030arXivmath/0509265WikidataQ56625087 ScholiaQ56625087MaRDI QIDQ3638693

Publication date: 28 October 2009

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509265

zbMATH Keywords

Hopf algebras set partitions monomial bases noncommutative symmetric functions set compositions noncommutative quasi-symmetric functions

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Hopf algebras and their applications (16T05) Connections of Hopf algebras with combinatorics (16T30)

Related Items (34)

Construction of dendriform trialgebras. ⋮ Cyclic Inclusion-Exclusion ⋮ Set partitions and integrable hierarchies ⋮ The module structure of the Solomon-Tits algebra of the symmetric group. ⋮ Pattern Hopf algebras ⋮ Schur functions in noncommuting variables ⋮ Some combinatorics related to central binomial coefficients: Grand-Dyck paths, coloured noncrossing partitions and signed pattern avoiding permutations ⋮ A Faà di Bruno subalgebra of the graded dual of word symmetric functions ⋮ A comodule-bialgebra structure for word-series substitution and mould composition ⋮ Mould calculus, polyhedral cones, and characters of combinatorial Hopf algebras. ⋮ Cumulants, spreadability and the Campbell-Baker-Hausdorff series ⋮ The Hopf algebra of finite topologies and mould composition ⋮ Hopf monoids, permutohedral cones, and generalized retarded functions ⋮ Scheduling problems ⋮ Basis of totally primitive elements of WQSym ⋮ Skew quasisymmetric Schur functions and noncommutative Schur functions ⋮ Combinatorial Hopf algebra of superclass functions of type \(D\). ⋮ Free and cofree Hopf algebras. ⋮ The antipode and primitive elements in the Hopf monoid of supercharacters ⋮ Strong forms of linearization for Hopf monoids in species ⋮ The monomial basis and the \(Q\)-basis of the Hopf algebra of parking functions. ⋮ Noncommutative unicellular LLT polynomials ⋮ From left modules to algebras over an operad: application to combinatorial Hopf algebras ⋮ The primitives and antipode in the Hopf algebra of symmetric functions in noncommuting variables ⋮ Chromatic symmetric functions in noncommuting variables revisited ⋮ Posets related to the connectivity set of Coxeter groups. ⋮ The antipode of linearized Hopf monoids ⋮ Unnamed Item ⋮ Trees, set compositions and the twisted descent algebra ⋮ The Hopf algebra of uniform block permutations. ⋮ Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras ⋮ A SUPERCHARACTER TABLE DECOMPOSITION VIA POWER-SUM SYMMETRIC FUNCTIONS ⋮ The kernel of chromatic quasisymmetric functions on graphs and hypergraphic polytopes ⋮ Hopf algebras of parking functions and decorated planar trees

Cites Work

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