Nathan Reading
Published 2011-09-23, updated 2011-10-05Version 2
In this chapter, we trace the path from the Tamari lattice, via lattice congruences of the weak order, to the definition of Cambrian lattices in the context of finite Coxeter groups, and onward to the construction of Cambrian fans. We then present sortable elements, the key combinatorial tool for studying Cambrian lattices and fans. The chapter concludes with a brief description of the applications of Cambrian lattices and sortable elements to Coxeter-Catalan combinatorics and to cluster algebras.
Comments: This is a chapter in an upcoming Tamari Festscrift. There have been minor changes since the first version posted
Eriksson's numbers game and finite Coxeter groups
The $ν$-Tamari lattice as the rotation lattice of $ν$-trees
Tamari lattices and noncrossing partitions in type B and beyond
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