Identities Derived from Noncrossing Partitions of Type $B$

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

doi:10.37236/616

William Y. C. Chen
Andrew Y. Z. Wang
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.