Rational noncrossing Coxeter–Catalan combinatorics
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.
Authors
- Pavel Galashin (ORCID: https://orcid.org/0000-0002-8109-4496)
- Nathan Williams (ORCID: https://orcid.org/0000-0003-2084-6428)
- Minh-Tâm Quang Trinh (ORCID: https://orcid.org/0000-0002-3013-8911)
- Thomas Lam (ORCID: https://orcid.org/0000-0003-2346-7685)
Institutions
- University of California, Los Angeles (US)
- The University of Texas at Dallas (US)
- University of Michigan (US)
- Yale University (US)
Publication Details
- Journal
- Proceedings of the London Mathematical Society
- Published
- 2024-10-01
- DOI
- https://doi.org/10.1112/plms.12643
- Citations
- 4
- Primary Topic
- Advanced Combinatorial Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 2.64
Funders
- National Science Foundation
- Simons Foundation