### The Characteristic Polynomials of Interpolations
between Coxeter Arrangements

We apply a lattice point counting method due to Blass and Sagan
to compute the characteristic polynomials for the subspace
arrangements interpolated between the Coxeter hyperplane
arrangements. Our proofs provide combinatorial interpretations
for the characteristic polynomials of such subspace arrangements.
In the process of doing this, we explore some interesting properties
of these
polynomials.