New interpretations for noncrossing partitions of classical types

Abstract

We interpret noncrossing partitions of type $B$ and type $D$ in terms of noncrossing partitions of type $A$. As an application, we get type-preserving bijections between noncrossing and nonnesting partitions of type $B$, type $C$ and type $D$ which are different from those in the recent work of Fink and Giraldo. We also define Catalan tableaux of type $B$ and type $D$, and find bijections between them and noncrossing partitions of type $B$ and type $D$ respectively.

21 pages, 15 figures, final version

References in corpus (3)

• Total positivity, Grassmannians, and networks
• Canopy of binary trees, Catalan tableaux and the asymmetric exclusion process
• The structure of alternative tableaux