Bijections between noncrossing and nonnesting partitions for classical reflection groups - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2009

Bijections between noncrossing and nonnesting partitions for classical reflection groups

Abstract

We present $\textit{type preserving}$ bijections between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis and Reiner. The bijections for the abstract Coxeter types $B$, $C$ and $D$ are new in the literature. To find them we define, for every type, sets of statistics that are in bijection with noncrossing and nonnesting partitions, and this correspondence is established by means of elementary methods in all cases. The statistics can be then seen to be counted by the generalized Catalan numbers Cat$(W)$ when $W$ is a classical reflection group. In particular, the statistics of type $A$ appear as a new explicit example of objects that are counted by the classical Catalan numbers.
Fichier principal
Vignette du fichier
dmAK0133.pdf (231 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

hal-01185429 , version 1 (20-08-2015)

Identifiers

Cite

Alex Fink, Benjamin Iriarte Giraldo. Bijections between noncrossing and nonnesting partitions for classical reflection groups. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.397-410, ⟨10.46298/dmtcs.2737⟩. ⟨hal-01185429⟩

Collections

INSMI TDS-MACS
87 View
506 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More