  A hyperplane arrangement in $\mathbb{R}^n$ is a finite collection of affine
hyperplanes. The regions are the connected components of the complement of
these hyperplanes. By a theorem of Zaslavsky, the number of regions of a
hyperplane arrangement is the sum of coefficients of its characteristic
polynomial. Arrangements that contain hyperplanes parallel to subspaces whose
defining equations are $x_i - x_j = 0$ form an important class called the
deformations of the braid arrangement. In a recent work, Bernardi showed that
regions of certain deformations are in one-to-one correspondence with certain
labeled trees. In this article, we define a statistic on these trees such that
the distribution is given by the coefficients of the characteristic polynomial.
In particular, our statistic applies to well-studied families like extended
Catalan, Shi, Linial and semiorder.
