ABSTRACT
In \cite{BS}, Bj\"orner and Sagan define certain subspace arrangements embedded in the Coxeter hyperplane arrangements of type $\cal B_n$ and $\cal D_n$. They give formulas for the exponential generating functions for the M\"obius function and for the characteristic polynomial for a class of subspace arrangements embedded in $\cal B_n$. The purpose of this paper is to give simpler proofs of those formulas and also to generalize to a much wider class of subspace arrangements. As a corollary the exponential generating function for the Euler characteristic is also calculated.