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<p>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 <i>B</i>.</p>

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Characteristic Polynomials of Deformations of Coxeter Arrangements Via Levels of Regions

  • 期刊论文

  • 发表日期：

    2026年3月21日

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  • Ningxin Zhang

摘要

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.