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 (2)

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

Cited by in corpus (1)

• Hopf algebras of diagrams