The characteristic polynomials of semigeneric threshold arrangements

Abstract

<abstract><p>The semigeneric threshold arrangement is the hyperplane arrangement defined by $ x_i+x_j = a_{i} $, where $ 1 \leq i < j \leq n $ and $ a_i\text{'s} $ are generic elements. In this paper, we obtain a necessary and sufficient condition for subarrangements of the semigeneric threshold arrangement to be central from the perspective of simple graphs. Combining it with Whitney's theorem, we provide a formula for the characteristic polynomials of the semigeneric threshold arrangement and its subarrangements.</p></abstract>