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arXiv · 1004.5208

Ordered forests, permutations and iterated integrals

Loic Foissy·Jeremie Unterberger
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Abstract

We construct an explicit Hopf algebra isomorphism from the algebra of heap-ordered trees to that of quasi-symmetric functions, generated by formal permutations, which is a lift of the natural projection of the Connes-Kreimer algebra of decorated rooted trees onto the shuffle algebra. This isomorphism gives a universal way of lifting measure-indexed characters of the Connes-Kreimer algebra into measure-indexed characters of the shuffle algebra, already introduced in \cite{Unterberger} in the framework of rough path theory as the so-called Fourier normal ordering algorithm.

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Loic Foissy, Jeremie Unterberger. 2010-04-29. Ordered forests, permutations and iterated integrals. https://arxiv.org/abs/1004.5208

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