Rooted Tree Maps

TL;DR

This paper introduces rooted tree maps derived from Hopf algebra of rooted trees, which generate relations among multiple zeta values, advancing understanding in algebraic structures related to number theory.

Contribution

It constructs a new class of linear maps on noncommutative polynomial algebra based on rooted trees and proves their role in relating multiple zeta values.

Findings

Rooted tree maps induce new relations among multiple zeta values.

The construction is based on Hopf algebra of rooted trees by Connes and Kreimer.

The maps provide a novel algebraic framework for studying multiple zeta values.

Abstract

Based on Hopf algebra of rooted trees introduced by Connes and Kreimer, we construct a class of linear maps on noncommutative polynomial algebra in two indeterminates, namely rooted tree maps. We also prove that their maps induce a class of relations among multiple zeta values.