# Some remarks on free arrangements

## TL;DR

This paper constructs a specific free subarrangement within a restricted Weyl arrangement of type E7 and confirms a recent conjecture about the characteristics of free and stair-free arrangements.

## Contribution

It introduces a particular free subarrangement of the E7 Weyl arrangement and proves a conjecture regarding free and stair-free arrangements.

## Key findings

- Identified a free subarrangement in the E7 Weyl arrangement
- Provided an affirmative answer to T. Abe's conjecture
- Enhanced understanding of free and stair-free arrangements

## Abstract

We exhibit a particular free subarrangement of a certain restriction of the Weyl arrangement of type $E_7$ and use it to give an affirmative answer to a recent conjecture by T.~Abe on the nature of additionally free and stair-free arrangements.