Geodesic
Colored trees and noncommutative symmetric functions
The electronic journal of combinatorics, Tome 17 (2010)

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Zbl arXiv EuDML
Let ${\cal CRF}_S$ denote the category of $S$-colored rooted forests, and H$_{{\cal CRF}_S}$ denote its Ringel-Hall algebra as introduced by Kremnizer and Szczesny. We construct a homomorphism from a $K^+_0({\cal CRF}_S)$–graded version of the Hopf algebra of noncommutative symmetric functions to H$_{{\cal CRF}_S}$. Dualizing, we obtain a homomorphism from the Connes-Kreimer Hopf algebra to a $K^+_0({\cal CRF}_S)$–graded version of the algebra of quasisymmetric functions. This homomorphism is a refinement of one considered by W. Zhao.
DOI : 10.37236/468
Classification : 05E05 
Matt Szczesny. Colored trees and noncommutative symmetric functions. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/468
@article{10_37236_468,
     author = {Matt Szczesny},
     title = {Colored trees and noncommutative symmetric functions},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/468},
     zbl = {1207.05215},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/468/}
}
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