Séminaire Lotharingien de Combinatoire, 93B.53 (2025), 12 pp.

Ningxin Zhang

Characteristic Polynomials of Deformations of Coxeter Arrangements via Levels of Regions

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

Received: November 15, 2024. Accepted: February 15, 2025. Final version: April 1, 2025.

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