A Noncommutative Symmetric System over the Grossman-Larson Hopf Algebra of Labeled Rooted Trees

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dc.creatorZhao, Wenhua
dc.date2005-09-07
dc.date2007-10-28
dc.date.accessioned2026-07-07T12:36:38Z
dc.date.available2026-07-07T12:36:38Z
dc.descriptionIn this paper, we construct explicitly a noncommutative symmetric (${\mathcal N}$CS) system over the Grossman-Larson Hopf algebra of labeled rooted trees. By the universal property of the ${\mathcal N}$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 ${\mathcal N}$CS system with the order polynomials of rooted trees is also given and proved.
dc.descriptionLatex, 30 pages. Following the referees' suggestions, several places have been improved. In particular, some diagrams of rooted trees have been added. To appear in J. Alg. Comb
dc.identifierhttps://arxiv.org/abs/math/0509136
dc.identifierhttp://arxiv.org/abs/math/0509136
dc.identifierJ. Alg. Comb. 28 (2008), 235--260.
dc.identifierdoi:10.1007/s10801-007-0100-5
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218159
dc.subjectCombinatorics
dc.subjectQuantum Algebra
dc.subject05E05, 16W30 (Primary); 06A07, 06A11 (Secondary)
dc.titleA Noncommutative Symmetric System over the Grossman-Larson Hopf Algebra of Labeled Rooted Trees
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