Characteristic and Ehrhart Polynomials

Let A be a subspace arrangement and let (A; t) be the characteristic polynomial of its intersection lattice L(A). We show that if the subspaces in A are taken from L(Bn), where Bn is the type B Weyl arrangement, then (A; t) counts a certain set of lattice points. This is the only known combinatorial interpretation of this polynomial in the subspace case. One can use this result to study the partial factorization of (A; t) over the integers and the coe cients of its expansion in various bases for the polynomial ring R[t]. Next we prove that the characteristic polynomial of any Weyl hyperplane arrangement can be expressed in terms of an Ehrhart quasi-polynomial for its a ne Weyl chamber. Note that our rst result deals with all subspace arrangements embedded in Bn while the second deals with all nite Weyl groups but only their hyperplane arrangements.