Geodesic
A noncommutative symmetric system over the Grossman-Larson Hopf algebra of labeled rooted trees
Journal of Algebraic Combinatorics, Tome 28 (2008) no. 2, pp. 235-260.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we construct explicitly a noncommutative symmetric ( $N$ mathcalN CS) system over the Grossman-Larson Hopf algebra of labeled rooted trees. By the universal property of the $N \mathcal $N CS system formed by the generating functions of certain noncommutative symmetric functions, we obtain a specialization of noncommutative symmetric functions by labeled rooted trees. Taking the graded duals, we also get a graded Hopf algebra homomorphism from the Connes-Kreimer Hopf algebra of labeled rooted forests to the Hopf algebra of quasi-symmetric functions. A connection of the coefficients of the third generating function of the constructed $N \mathcal $N CS system with the order polynomials of rooted trees is also given and proved.
Keywords: keywords noncommutative symmetric functions, grossman-larson Hopf algebra, Connes-kreimer Hopf algebras, labeled rooted trees 
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     author = {Zhao, Wenhua},
     title = {A noncommutative symmetric system over the {Grossman-Larson} {Hopf} algebra of labeled rooted trees},
     journal = {Journal of Algebraic Combinatorics},
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Zhao, Wenhua. A noncommutative symmetric system over the Grossman-Larson Hopf algebra of labeled rooted trees. Journal of Algebraic Combinatorics, Tome 28 (2008) no. 2, pp. 235-260. http://geodesic.mathdoc.fr/item/JAC_2008__28_2_a4/