Enumerating chambers of hyperplane arrangements with symmetry

Taylor Brysiewicz, Holger Eble, and Lukas Kühne

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Submission date: 01. Jun. 2021
Pages: 21
Bibtex
MSC-Numbers: 52C35, 52B15
Keywords and phrases: hyperplane arrangement, Chambers, Symmetry reduction
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Link to arXiv: See the arXiv entry of this preprint.

Abstract:
We introduce a new algorithm for enumerating chambers 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.