The characteristic polynomials of semigeneric threshold arrangements.

The semigeneric threshold arrangement is the hyperplane arrangement defined by x_i + x_j = ai, where 1 ≤ i < j ≤ n and ai'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. [ABSTRACT FROM AUTHOR]