Consider the coradical filtration of the Hopf algebras of planar binary trees
of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We show
that the associated graded Hopf algebras are dual to the cocommutative Hopf
algebras introduced in the late 1980's by Grossman and Larson. These Hopf
algebras are constructed from ordered trees and heap-ordered trees,
respectively. We also show that whenever one starts from a Hopf algebra that is
a cofree graded coalgebra, the associated graded Hopf algebra is a shuffle Hopf
algebra. This implies that the Hopf algebras of ordered trees and heap-ordered
trees are tensor Hopf algebras.