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Sortable elements and Cambrian lattices

Nathan Reading
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Abstract

We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this congruence as the Cambrian congruence on W, so that the Cambrian lattice is the weak order on Coxeter-sortable elements. These results exhibit W-Catalan combinatorics arising in the context of the lattice theory of the weak order on W.

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Nathan Reading. 2005-12-14. Sortable elements and Cambrian lattices. https://doi.org/10.1007/s00012-007-2009-1

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