Return to Revisions

The Catalan numbers you get in types other than A depend on which interpretation of the Catalan numbers you are generalizing. There are at least two possibilities: the number of anti-chains in the root poset (these are sometimes called non-nesting partitions) gives the so called Coxeter-Catalan number; these are well-studied, see e.g. "A uniform bijection between nonnesting and noncrossing partitions" by Armstrong, Stump, and Thomas; the number of Stembridge's "fully commutative" elements (in type A, this is the same as 321-avoiding permutations) of the Weyl group is another generalization which gives different numbers.