The characteristic polynomials of subarrangements of Coxeter arrangements

AbstractWe 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 Bn, Dn, and A>−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