Consider the collection of hyperplanes in $mathbb{R}^n$ whose defining equations are given by ${x_i + x_j = 0mid 1leq i<jleq n}$. This arrangement is called the threshold arrangement since its regions are in bijection with labeled threshold graphs on $n$ vertices. Zaslavskys 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.
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