The shuffle relation of fractions from multiple zeta values

TL;DR

This paper reveals that a class of fractions related to multiple zeta values has a shuffle algebra structure, unifying different methods used in their study and providing explicit product formulas.

Contribution

It introduces a natural shuffle algebra structure for fractions associated with MZVs, connecting various existing methods and offering explicit product formulas.

Findings

Fractions from MZVs form a shuffle algebra

Unifies shuffle, stuffle, and partial fraction methods

Provides explicit product formulas for these fractions

Abstract

Partial fraction methods play an important role in the study of multiple zeta values. One class of such fractions is related to the integral representations of MZVs. We show that this class of fractions has a natural structure of shuffle algebra. This finding conceptualizes the connections among the various methods of stuffle, shuffle and partial fractions in the study of MZVs. This approach also gives an explicit product formula of the fractions.