Identities Derived from Noncrossing Partitions of Type $B$

  • William Y. C. Chen
  • Andrew Y. Z. Wang
  • Alina F. Y. Zhao
DOI: https://doi.org/10.37236/616

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.

Published
2011-06-14
How to Cite
Chen, W. Y. C., Wang, A. Y. Z., & Zhao, A. F. Y. (2011). Identities Derived from Noncrossing Partitions of Type $B$. The Electronic Journal of Combinatorics, 18(1), P129. https://doi.org/10.37236/616
Issue
Volume 18, Issue 1 (2011)
Article Number
P129