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- W1987706087 abstract "Consider the coradical filtrations of the Hopf algebras of planar binary trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We give explicit isomorphisms showing 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. These results follow from the fact that whenever one starts from a Hopf algebra that is a cofree graded coalgebra, the associated graded Hopf algebra is a shuffle Hopf algebra." @default.
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- W1987706087 date "2005-12-01" @default.
- W1987706087 modified "2023-09-23" @default.
- W1987706087 title "Cocommutative Hopf Algebras of Permutations and Trees" @default.
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- W1987706087 doi "https://doi.org/10.1007/s10801-005-4628-y" @default.
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