Characteristic Polynomials of Deformations of Coxeter Arrangements via levels of regions

2024/11/06 by Ningxin Zhang, Zhang, Ningxin · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2411.03756

openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a novel formula for characteristic polynomials of deformations of the Braid arrangement using the notion of levels of regions. As an application, we recover and strengthen results of Chen et al. on the characteristic polynomial of several specific types of hyperplane arrangements via much simpler arguments. Our theorem also generalizes to type B.

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• Region level via centralization for hyperplane arrangements and beyond

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