Clusters, Coxeter-sortable elements and noncrossing partitions

• Autores: Nathan Reading
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 12, 2007, págs. 5931-5958
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04319-x
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• Resumen

  • We introduce Coxeter-sortable elements of a Coxeter group For finite 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