Clusters, Coxeter-sortable elements and noncrossing partitions

Details Clusters, Coxeter-sortable elements and noncrossing partitions Clusters, Coxeter-sortable elements and noncrossing partitions

2005-07-08

arxiv.org/abs/math/0507186v2

Mathematics

Combinatorics

Minor changes in exposition, including: More precise statement in Remark 6.8; Added Remark 6.9, an observation which is helpfu

Scientific paper

We introduce Coxeter-sortable elements of a Coxeter group W. For finite W, we
give bijective proofs that Coxeter-sortable elements are equinumerous with
clusters and with noncrossing partitions. We characterize Coxeter-sortable
elements in terms of their inversion sets and, in the classical cases, in terms
of permutations.

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