%0 Journal Article
%T Sortable elements and Cambrian lattices
%A Nathan Reading
%J Mathematics
%D 2005
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0512339v1