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.