Shuffle product formulas of multiple zeta values

TL;DR

This paper explores shuffle product formulas for multiple zeta values, providing new combinatorial proofs and reformulations for general and restricted cases involving multiple zeta values.

Contribution

It introduces new shuffle product formulas for multiple zeta values using combinatorial methods, including general and restricted cases for products of two or more values.

Findings

Proved a general shuffle product formula for two multiple zeta values.

Reformulated several restricted shuffle product formulas.

Extended shuffle product formulas to products of n multiple zeta values.

Abstract

Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted shuffle product formulas of the product of two multiple zeta values, and a restricted shuffle product formula of the product of $n$ multiple zeta values.