Sách Colored trees and noncommutative symmetric functions

Abstract
Let C RF S denote the category of S-colored rooted forests, and HC RF S
denote
its Ringel-Hall algebra as introduced in [6]. We construct a homomorphism from a
K
+
0
(C RF S)–graded version of the Hopf algebra of noncommutative symmetric func-
tions to HC RF S
. Dualizing, we obtain a homomorphism from the Connes-Kreimer
Hopf algebra to a K
+
0
(C RF S)–graded version of the algebra of quasisymmetric
functions. This homomorphism is a refinement of one considered by W. Zhao in [9].