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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APA
Reading, N. (2006). Clusters, Coxeter-sortable elements and noncrossing partitions. In FPSAC 2006 - Proceedings: 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics (pp. 275–281). https://doi.org/10.1090/s0002-9947-07-04319-x
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