New interpretations for noncrossing partitions of classical types

TL;DR

This paper provides new interpretations of noncrossing partitions of classical types B and D in terms of type A, establishing bijections with nonnesting partitions and defining Catalan tableaux for these types.

Contribution

It introduces novel interpretations and bijections for noncrossing partitions of types B and D, differing from previous work, and defines Catalan tableaux for these types.

Findings

Type-preserving bijections between noncrossing and nonnesting partitions of types B, C, D

New interpretations of noncrossing partitions of types B and D in terms of type A

Definition of Catalan tableaux of types B and D with bijections to noncrossing partitions

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.