Identities Derived from Noncrossing Partitions of Type $B$

  • William Y. C. Chen
  • Andrew Y. Z. Wang
  • Alina F. Y. Zhao


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.

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