Work

Rational Catalan numbers for complex reflection groups

Year: 2025

Type: article

Abstract: Assuming standard conjectures, we show that the canonical symmetrizing trace on the Hecke algebra of irreducible spetsial complex reflection groups produces rational Catalan numbers when evaluated at powers of a Coxeter element. 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.

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2025.01.027

Author: Weston Miller

Institution: The University of Texas at Dallas

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310

Funder: National Science Foundation