Computing characteristic polynomials of hyperplane arrangements with symmetries

TL;DR

This paper presents a novel algorithm that leverages symmetry groups to efficiently compute the characteristic polynomials of hyperplane arrangements, also providing chamber counts as a byproduct, with applications demonstrated in physics and computer science.

Contribution

The paper introduces a new symmetry-exploiting algorithm for hyperplane arrangements, implemented in Julia, improving computational efficiency and enabling practical applications.

Findings

Efficient computation of characteristic polynomials using symmetry groups.

Successful implementation in Julia demonstrating practical applications.

Chamber counting as a byproduct of the algorithm.

Abstract

We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers of an arrangement as a byproduct of computing its characteristic polynomial. We showcase our julia implementation, based on OSCAR, on examples coming from hyperplane arrangements with applications to physics and computer science.