Let A be a subspace arrangement and let chi(A,t) be the characteristic
polynomial of its intersection lattice L(A). We show that if the subspaces in A
are taken from L(B_n), where B_n is the type B Weyl arrangement, then chi(A,t)
counts a certain set of lattice points. One can use this result to study the
partial factorization of chi(A,t) over the integers and the coefficients 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 affine Weyl chamber. Note that
our first result deals with all subspace arrangements embedded in B_n while the
second deals with all finite Weyl groups but only their hyperplane
arrangements.Comment: 16 pages, 1 figure, Latex, to be published in J. Alg. Combin. see
related papers at http://www.math.msu.edu/~saga
