Enumerating Chambers of Hyperplane Arrangements with Symmetry

This page contains auxiliary material to the paper:
Taylor Brysiewicz, Holger Eble, and Lukas Kühne: Enumerating chambers of hyperplane arrangements with symmetry
../_images/running_example_Single.png

The above picture shows an example of a hyperplane arrangement in the plane consisting of four hyperplanes. The complement consists of ten chambers.

One way of counting these chambers is through a deletion-restriction tree depicted below.

../_images/running_example.png

Our paper outlines a novel algorithm to count chambers of hyperplane arrangments taking advantage their symmetry. This yields the following reduced algorithmic structure.

../_images/running_example_Alg2Groups.png

Our chamber counting algorithm is implemented in julia using OSCAR.jl. It can perform this task for arrangements with over a quadrillion chambers. Our implementation is publicly available here: CountingChambers.jl.

The following Jupyter notebooks illustrate how to use our software.

You may also run this file online yourself by clicking the link below.

../_images/binder_badge.svg

Project page created: 25/05/2021

Project contributors: Taylor Brysiewicz, Holger Eble, and Lukas Kühne

Corresponding author of this page: Lukas Kühne, lukas.kuhne@mis.mpg.de

Software used: Julia (Version 1.6.0)