# MAT-free reflection arrangements

## TL;DR

This paper introduces and classifies MAT-free and MAT2-free hyperplane arrangements, expanding understanding of their structure and relation to other free arrangements in complex reflection groups.

## Contribution

It defines new classes of free arrangements based on the Multiple Addition Theorem and provides classifications for irreducible complex reflection arrangements.

## Key findings

- Classified irreducible complex reflection arrangements as MAT-free or MAT2-free.
- Connected MAT-free arrangements to the structure of complex reflection groups.
- Explored relationships between MAT-free arrangements and other free arrangement classes.

## Abstract

We introduce the class of MAT-free hyperplane arrangements which is based on the Multiple Addition Theorem by Abe, Barakat, Cuntz, Hoge, and Terao. We also investigate the closely related class of MAT2-free arrangements based on a recent generalization of the Multiple Addition Theorem by Abe and Terao. We give classifications of the irreducible complex reflection arrangements which are MAT-free respectively MAT2-free. Furthermore, we ask some questions concerning relations to other classes of free arrangements.