Rooted tree maps and the derivation relation for multiple zeta values

TL;DR

This paper demonstrates that derivation relations for multiple zeta values are encompassed within the linear relations generated by rooted tree maps derived from the Connes-Kreimer Hopf algebra.

Contribution

It establishes that derivation relations for multiple zeta values are a subset of the linear relations induced by rooted tree maps.

Findings

Derivation relations are contained in rooted tree map relations.

Rooted tree maps generate a broad class of linear relations for multiple zeta values.

The approach connects Hopf algebra structures with multiple zeta value relations.

Abstract

Rooted tree maps assign to an element of the Connes-Kreimer Hopf algebra of rooted trees a linear map on the noncommutative polynomial algebra in two letters. Evaluated at any admissible word these maps induce linear relations between multiple zeta values. In this note we show that the derivation relations for multiple zeta values are contained in this class of linear relations.