Combinatorial remarks on the cyclic sum formula for multiple zeta values

TL;DR

This paper investigates the cyclic sum formula for multiple zeta values, providing combinatorial analysis to classify and count the relations within different strata defined by specific linear operators.

Contribution

It introduces a combinatorial approach to stratify and enumerate relations in the cyclic sum formula for multiple zeta values using linear operators.

Findings

Number of relations in each stratum determined

Combinatorial methods applied to classify relations

Enhanced understanding of the structure of multiple zeta value relations

Abstract

The multiple zeta values are generalizations of the values of the Riemann zeta function at positive integers. They are known to satisfy a number of relations, among which are the cyclic sum formula. The cyclic sum formula can be stratified via linear operators defined by the second and third authors. We give the number of relations belonging to each stratum by combinatorial arguments.