The connector for Double Ohno relation

TL;DR

This paper introduces a new connector that generalizes previous work, providing a direct proof of the double Ohno relation and extending it to a broader class of relations involving ($q$-)parameters.

Contribution

The paper presents a novel connector that unifies and generalizes existing relations, offering a new proof and broader generalizations in the theory of multiple zeta values.

Findings

Provided a direct proof of the double Ohno relation.

Established a simultaneous generalization of ($q$-)Ohno and ($q$-)double Ohno relations.

Introduced a new connector that unifies previous relations.

Abstract

In this paper, we introduce a new connector which generalizes the connector found by the third author and Yamamoto. The new connector gives a direct proof of the double Ohno relation recently proved by the first author, the second author, Murahara, and Onozuka. Furthermore, we obtain a simultaneous generalization of the ($q$-)Ohno relation and the ($q$-)double Ohno relation.