Chains in the Noncrossing Partition Lattice
Chains in the Noncrossing Partition Lattice
We establish recursions counting various classes of chains in the noncrossing partition lattice of a finite Coxeter group. The recursions specialize a general relation which is proven uniformly (i.e., without appealing to the classification of finite Coxeter groups) using basic facts about noncrossing partitions. We solve these recursions for each …