Identity Families of Multiple Harmonic Sums and Multiple Zeta (Star) Values

TL;DR

This paper introduces new identity families for multiple harmonic sums and applies them to prove several conjectures related to multiple zeta star values, advancing understanding of their algebraic structure.

Contribution

It presents novel identities for multiple harmonic sums and uses them to prove key conjectures about multiple zeta star values, including the Two-one formula.

Findings

Proved the Two-one formula conjectured by Ohno and Zudilin.

Validated several conjectures involving 2-3-2-1 type MZSV.

Established new identity families generalizing recent results.

Abstract

In this paper we present many new families of identities for multiple harmonic sums using binomial coefficients. Some of these generalize a few recent results of Hessami Pilehrood et al. As applications we prove several conjectures involving multiple zeta star values (MZSV): the Two-one formula conjectured by Ohno and Zudilin, and a few conjectures of Imatomi et al. involving 2-3-2-1 type MZSV, where 2 means some finite string of 2's