(Non)commutative Hopf algebras of trees and (quasi)symmetric functions
Michael E. HoffmanUnited States Naval Academy, Annapolis, USA
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The Connes–Kreimer Hopf algebra of rooted trees, its dual, and the Foissy Hopf algebra 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.