Rational Catalan Numbers for Complex Reflection Groups
arXiv:2310.12354 · doi:10.1016/j.jalgebra.2025.01.027
Abstract
Assuming standard conjectures, we show that the canonical symmetrizing trace evaluated at powers of a Coxeter element produces rational Catalan numbers for irreducible spetsial complex reflection groups. This extends a technique used by Galashin, Lam, Trinh, and Williams to uniformly prove the enumeration of their noncrossing Catalan objects for finite Coxeter groups.
28 pages, 2 figures