Work

Rational noncrossing Coxeter–Catalan combinatorics

Year: 2024

Type: article

Abstract: We solve two open problems in Coxeter–Catalan combinatorics. First, we introduce a family of rational noncrossing objects for any finite Coxeter group, using the combinatorics of distinguished subwords. Second, we give a type‐uniform proof that these noncrossing Catalan objects are counted by the rational Coxeter–Catalan number, using the character theory of the associated Hecke algebra and the properties of Lusztig's exotic Fourier transform. We solve the same problems for rational noncrossing parking objects.

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.12643

Authors: Pavel Galashin, Thomas Lam, Minh‐Tâm Trinh, Nathan Williams

Institutions: University of California, Los Angeles, University of Michigan, Yale University, 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: green

Funders: National Science Foundation, Simons Foundation