Clusters, Coxeter-sortable elements and noncrossing partitions

Reading, Nathan

doi:10.1090/S0002-9947-07-04319-X

Clusters, Coxeter-sortable elements and noncrossing partitions
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Trans. Amer. Math. Soc. 359 (2007), 5931-5958

Abstract:

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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