Arslan, HasanCan, Himmet2021-11-112021-11-112020-06-30https://doi.org/10.31801/cfsuasmas.599246http://hdl.handle.net/20.500.12575/75985In this paper, we firstly give an alternative method to determine the size of C ( S n ) which is the set of elements of type S n in a finite Coxeter system ( W n , S n ) of type B n . We also show that all cuspidal classes of W n are actually the conjugate classes K λ for every λ ∈ D P + ( n ) . We then define the generalized Burnside algebra H B ( W n ) for W n and construct a surjective algebra morphism between H B ( W n ) and Mantaci-Reutenauer algebra M R ( W n ) . We obtain a set of orthogonal primitive idempotents e λ , λ ∈ D P ( n ) of H B ( W n ) , that is, all the characteristic class functions of W n . Finally, we give an effective formula to compute the number of elements of all the conjugate classes K λ , λ ∈ D P ( n ) of W n .enCuspidal ClassMantaci-Reutenauer AlgebraBurnside AlgebraArticle6912522652618-6470