From the Tamari lattice to Cambrian lattices and beyond

Details From the Tamari lattice to Cambrian lattices and beyond From the Tamari lattice to Cambrian lattices and beyond

2011-09-23

arxiv.org/abs/1109.5105v2

Mathematics

Combinatorics

This is a chapter in an upcoming Tamari Festscrift. There have been minor changes since the first version posted

Scientific paper

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.

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