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arXiv · 0710.3739

(Non)Commutative Hopf algebras of trees and (quasi)symmetric functions

Michael E. Hoffman
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Abstract

The Connes-Kreimer Hopf algebra of rooted trees, its dual, and the Foissy Hopf algebra of of planar rooted trees are related to each other and to the well-known Hopf algebras of symmetric and quasi-symmetric functions via a pair of commutative diagrams. We show how this point of view can simplify computations in the Connes-Kreimer Hopf algebra and its dual, particularly for combinatorial Dyson-Schwinger equations.

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Michael E. Hoffman. 2007-10-19. (Non)Commutative Hopf algebras of trees and (quasi)symmetric functions. https://arxiv.org/abs/0710.3739

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