A unified approach to qMZVs

TL;DR

This survey introduces a comprehensive framework for q-analogues of multiple zeta values, unifying various models and translation methods, and proposing marked partitions as a new approach.

Contribution

It provides a unified setup for different qMZV models, including translation techniques and the novel concept of marked partitions.

Findings

Unified framework for qMZV models

Translation methods between models

Introduction of marked partitions

Abstract

This survey gives a self-contained introduction to q-analogues of multiple zeta values (qMZVs). For this, we consider most common models of qMZVs in a unified setup going back to Bachmann and K\"uhn, such as a related quasi-shuffle product each. Also, we give distinguished translations between several models. As another unified approach to qMZVs, we introduce the concept of marked partitions.