Arborified Multiple Zeta Values

  • Dominique ManchonEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 314)


We describe some particular finite sums of multiple zeta values which arise from J. Ecalle’s “arborification”, a process which can be described as a surjective Hopf algebra morphism from the Hopf algebra of decorated rooted forests onto a Hopf algebra of shuffles or quasi-shuffles. This formalism holds for both the iterated sum picture and the iterated integral picture. It involves a decoration of the forests by the positive integers in the first case, by only two colours in the second case.


Multiple zeta values Rooted trees Hopf algebras Shuffle Quasi-shuffle Arborification 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.C.N.R.S. UMR 6620AubièreFrance

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