The Characteristic Polynomials of Subarrangements of Coxeter Arrangements

We apply a lattice point counting method due to Blass and Sagan to compute the characteristic polynomials for $k$-equal subspace arrangements, the interpolations between the Coxeter hyperplane arrangements $\cB_n$, $\cD_n$, and $\cA_{n-1}$, and the related $l,h$-equal and $l,h,f$-equal subspace arrangements. Our proofs provide combinatorial interpretations for the characteristic polynomials of these subspace arrangements. As a result, we are able to explore the interesting properties of these polynomials.