The Characteristic Polynomials of Interpolations between Coxeter Arrangements

We apply a lattice point counting method due to Blass and Sagan [2] 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.