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Clusters, Coxeter-sortable elements and noncrossing partitions
Nathan Reading
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Source: Crossref
Published: Jun 27, 2007
DOI: 10.1090/s0002-9947-07-04319-x
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We introduce Coxeter-sortable elements of a Coxeter group W . W. For finite W , 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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