Identities Derived from Noncrossing Partitions of Type B

William Y. C. Chen, Andrew Y. Z. Wang and Alina F. Y. Zhao

  Abstract:  Based on weighted noncrossing partitions of type B, we obtain type B analogues of Coker’s identities on the Narayana polynomials. A parity reversing involution is given for the alternating sum of Narayana numbers of type B. Moreover, we find type B analogues of the refinements of Coker’s identities due to Chen, Deutsch and Elizalde. By combinatorial constructions, we provide type B analogues of three identities of Mansour and Sun also on the Narayana polynomials.

  AMS Classification:  05A15, 05A19

  Keywords:  noncrossing partition of type B, Narayana polynomial of type B, bijection.

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