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Journal Articles International Mathematics Research Notices Year : 2013

Ordered forests, permutations and iterated integrals

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.

Dates and versions

hal-00479037 , version 1 (30-04-2010)

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Loic Foissy, Jeremie Unterberger. Ordered forests, permutations and iterated integrals. International Mathematics Research Notices, 2013, 4, pp.846-885. ⟨10.1093/imrn/rnr273⟩. ⟨hal-00479037⟩
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