A Generalization of an Alternating Sum Formula for Finite Coxeter Groups

For W a finite Coxeter group, a formula is found for the size of W equivalence classes of subsets of a base. The proof is a case-by-case analysis using results and tables of Carter and Orlik/Solomon. As a corollary we obtain an alternating sum identity which generalizes a well-known identity from the theory of Coxeter groups.