Diamond lift of Hirose--Sato's formula involving the Hoffman basis

TL;DR

This paper provides a new proof of Hirose--Sato's formula for multiple zeta values involving the Hoffman basis, utilizing the drop 1 relation to simplify the expansion process.

Contribution

It introduces a novel proof technique for Hirose--Sato's formula using the drop 1 relation, enhancing understanding of multiple zeta value expansions.

Findings

New proof of Hirose--Sato's formula using the drop 1 relation

Simplifies the expansion of specific multiple zeta values

Deepens the connection between the Hoffman basis and zeta value formulas

Abstract

In this paper, we give a new proof of Hirose--Sato's formula for the expansion of $\zeta(\{2\}^{a_1-1},3,\dots,\{2\}^{a_r-1},3,\{2\}^{c-1},1,\{2\}^{b_1},\dots, 1,\{2\}^{b_s})$ in the Hoffman basis, using the drop 1 relation.