# On the duality and the derivation relations for multiple zeta values

## TL;DR

This paper explores the connection between duality and derivation relations in multiple zeta values, showing that certain duality relations can be derived from the extended double shuffle relation, thus deepening understanding of their algebraic structure.

## Contribution

It demonstrates that duality relations for double zeta values and specific sums of multiple zeta values are derivable from the derivation relation within the extended double shuffle framework.

## Key findings

- Duality for double zeta values is deducible from derivation relations.
- Duality for sums of multiple zeta values with initial 2's is also derivable.
- Enhances understanding of the algebraic relations among multiple zeta values.

## Abstract

We consider the problem of deducing the duality relation from the extended double shuffle relation for multiple zeta values. Especially we prove that the duality relation for double zeta values and that for the sum of multiple zeta values whose first components are 2's are deduced from the derivation relation, which is known as a subclass of the extended double shuffle relation.