Rational Noncrossing Coxeter-Catalan Combinatorics
Combinatorics
2022-08-02 v1 Representation Theory
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.
Cite
@article{arxiv.2208.00121,
title = {Rational Noncrossing Coxeter-Catalan Combinatorics},
author = {Pavel Galashin and Thomas Lam and Minh-Tâm Quang Trinh and Nathan Williams},
journal= {arXiv preprint arXiv:2208.00121},
year = {2022}
}
Comments
42 pages