Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Colored trees and noncommutative symmetric functions   Let $\CRF_S$ denote the category of $S$-colored rooted forests, and
$\H_{\CRF_S}$ denote its Ringel-Hall algebra as introduced in \cite{KS}. We
construct a homomorphism from a $K^+_0 (\CRF_S)$--graded version of the Hopf
algebra of noncommutative symmetric functions to $\H_{\CRF_S}$. Dualizing, we
obtain a homomorphism from the Connes-Kreimer Hopf algebra to a $K^+_0
(\CRF_S)$--graded version of the algebra of quasisymmetric functions. This
homomorphism is a refinement of one considered by W. Zhao in \cite{Z}.

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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio