The Characteristic polynomials of semigeneric graphical arrangements

Abstract

<abstract><p>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 $ \mathcal{S}_G: = \{x_i- x_j = a_i: ij\in E(G), 1\leq i &lt; j\leq n \} $, where $ a_i{\rm{'s}} $ are generic. The formula is obtained by characterizing central subarrangements of $ \mathcal{S}_{G} $ via the corresponding graph $ {G} $.</p></abstract>