New interpretations for noncrossing partitions of classical types

Jang Soo Kim

New interpretations for noncrossing partitions of classical types

Combinatorics 2011-08-30 v2

Authors: Jang Soo Kim

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.

Keywords

noncrossing partitions nonnesting partitions Catalan tableaux type-preserving bijections classical types Coxeter groups

Cite

@article{arxiv.0910.2036,
  title  = {New interpretations for noncrossing partitions of classical types},
  author = {Jang Soo Kim},
  journal= {arXiv preprint arXiv:0910.2036},
  year   = {2011}
}

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21 pages, 15 figures, final version

New interpretations for noncrossing partitions of classical types

Abstract

Keywords

Cite

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