Linear relations of Ohno sums of multiple zeta values

TL;DR

This paper explores new linear relations among Ohno sums of multiple zeta values, extending known relations and proposing conjectures for further unexplored relations.

Contribution

It introduces two new families of $Q$-linear relations among Ohno sums beyond Ohno's original relations and suggests several conjectural families.

Findings

Proved two new families of linear relations among Ohno sums.

Identified relations not contained in Ohno's original relation.

Proposed conjectural families for future research.

Abstract

Ohno's relation is a well-known family of relations among multiple zeta values, which can naturally be regarded as a type of duality for a certain power series which we call an Ohno sum. In this paper, we investigate $\mathbb{Q}$-linear relations among Ohno sums which are not contained in Ohno's relation. We prove two new families of such relations, and pose several further conjectural families of such relations.