Polynomial realizations of some trialgebras

Abstract

We realize several combinatorial Hopf algebras based on set compositions, plane trees and segmented compositions in terms of noncommutative polynomials in infinitely many variables. For each of them, we describe a trialgebra structure, an internal product, and several bases.

12 pages, LaTEX, to be presented at FPSAC'06

References in corpus (3)

• A Hopf algebra of parking functions
• Construction of dendriform trialgebras
• Weak Bruhat order on the set of faces of the permutahedra

Cited by in corpus (16)

• Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
• New identities in dendriform algebras
• Rota-Baxter algebras and new combinatorial identities
• Hopf Algebras and Markov Chains
• Combinatorial Hopf algebra structure on packed square matrices
• Polynomial realizations of some combinatorial Hopf algebras
• Mould calculus, polyhedral cones, and characters of combinatorial Hopf algebras
• Hopf algebras of diagrams
• Commutative and non-commutative bialgebras of quasi-posets and applications to Ehrhart polynomials
• Permutation statistics related to a class of noncommutative symmetric functions and generalizations of the Genocchi numbers
• Bialgebras for Stanley symmetric functions
• Shifted combinatorial Hopf algebras from $K$-theory
• Powersum Bases in Quasisymmetric Functions and Quasisymmetric Functions in Non-commuting Variables
• A theory of pictures for quasi-posets
• The # product in combinatorial Hopf algebras
• Basis of totally primitive elements of WQSym