@article{Gao2023, 
author = {Ruimei Gao and Jingjing Qiang and Miao Zhang},
title = {The Characteristic polynomials of semigeneric graphical arrangements},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {2},
pages = {3226-3235},
keywords = {hyperplane arrangement, characteristic polynomial, semigeneric graphical arrangement, semigeneric braid arrangement, generic element},
url = {https://www.sciopen.com/article/10.3934/math.2023166},
doi = {10.3934/math.2023166},
abstract = {The purpose of this paper is twofold. Firstly, we generalize the notion of semigeneric braid arrangement to semigeneric graphical arrangement. Secondly, we give a formula for the characteristic polynomial of the semigeneric graphical arrangement              S        G    :=  {      x    i    −      x    j    =      a    i    :  i  j  ∈  E  (  G  )  ,  1  ≤  i  <  j  ≤  n  }, where        a    i                              ′            s       are generic. The formula is obtained by characterizing central subarrangements of              S              G       via the corresponding graph        G  .}
}