Browsing by Author "Can, Himmet"

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    Generalized Burnside algebra of type B_{n}
    (Ankara Üniversitesi Fen Fakültesi, 2020-06-30) Arslan, Hasan; Can, Himmet; Other; Other
    In 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 .