Restricted sum formula and derivation relation for multiple zeta values

TL;DR

This paper demonstrates that the derivation relation for multiple zeta values implies the restricted sum formula, establishing a connection between two algebraic relations in the study of multiple zeta values.

Contribution

The paper proves that the derivation relation implies the restricted sum formula for multiple zeta values, linking two previously known algebraic relations.

Findings

Derivation relation implies the restricted sum formula

Algebraic relations for multiple zeta values are interconnected

Provides a new proof linking two key relations

Abstract

Two classes of relations for multiple zeta values are handled algebraically. A restricted sum formula is proved by Eie, Liaw and Ong. The derivation relation is proved by Ihara, Kaneko and Zagier. In this paper we show the latter implies the former.