  Consider the collection of hyperplanes in $\mathbb{R}^n$ whose defining
equations are given by $\{x_i + x_j = 0\mid 1\leq i<j\leq n\}$. This
arrangement is called the threshold arrangement since its regions are in
bijection with labeled threshold graphs on $n$ vertices. Zaslavsky's theorem
implies that the number of regions of this arrangement is the sum of
coefficients of the characteristic polynomial of the arrangement. In the
present article we give a combinatorial meaning to these coefficients as the
number of labeled threshold graphs with a certain property, thus answering a
question posed by Stanley.
