### 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.