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math.NT2026
Regularised double shuffle relations for planar Arborified Zeta Values
Pierre Catoire, Pierre J. Clavier, Ku-Yu Fan
We endow spaces of decorated planar rooted trees with new dendriform and tridendrifrom algebra structures and provide their combinatorial description. We then show that the planar…
math.NT2022
Generalisations of multiple zeta values to rooted forests
Pierre J. Clavier, Dorian Perrot
We show that any convergent (shuffle) arborified zeta value admits a series representation. This justifies the introduction of a new generalisation to rooted forests of multiple ze…
math.NT2018★ 3 cited
Double shuffle relations for arborified zeta values
Pierre J. Clavier
Arborified zeta values are defined as iterated series and integrals using the universal properties of rooted trees. This approach allows to study their convergence domain and to re…