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 Orlik and Solomon. As a corollary we obtain an alternating sum identity which generalizes a well-known identity from the theory of Coxeter groups. 


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