Sortable elements and Cambrian lattices

Details Sortable elements and Cambrian lattices Sortable elements and Cambrian lattices

2005-12-14

arxiv.org/abs/math/0512339v1

Mathematics

Combinatorics

23 pages, 9 figures

Scientific paper

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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