# Double shuffle relations for arborified zeta values

## TL;DR

This paper introduces arborified zeta values, explores their algebraic properties using rooted trees, and relates them to multizeta values, expanding the algebraic framework with new product structures.

## Contribution

It defines and studies rooted tree-based generalizations of shuffle and stuffle products, proving arborified zeta values form algebra morphisms for these products.

## Key findings

- Established convergence domains for arborified zeta values
- Related arborified zeta values to classical multizeta values
- Proved algebraic morphism properties for new tree-based products

## Abstract

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 relate them to multizeta values. Generalisations to rooted trees of the stuffle and shuffle products are defined and studied. It is further shown that arborifed zeta values are algebra morphisms for these new products on trees.