Sortable elements and Cambrian lattices

2005/12/14 by Reading, Nathan · 1 citation
#06B10 #20F55 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0512339

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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