Séminaire Lotharingien de Combinatoire, 91B.44 (2024), 12 pp.

Weston Miller

Rational Catalan Numbers for Complex Reflection Groups

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.

Received: November 15, 2023. Accepted: February 15, 2024. Final version: April 1, 2024.

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