Computing characteristic polynomials of hyperplane arrangements with symmetries

2021/05/30 by Taylor Brysiewicz, Brysiewicz, Taylor, Holger Eble +3 · 2 citations
Computer Science · Engineering · Mathematics · #52B15 #52C35 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #G.2.1 #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2105.14542

openalex publication_date 2021/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Nakajima quiver varieties in dimension four
• Combinatorics of slices of cubes

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