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arXiv · 2208.00121

Rational Noncrossing Coxeter-Catalan Combinatorics

Pavel Galashin·Thomas Lam·Minh-Tâm Quang Trinh·Nathan Williams
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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.

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Pavel Galashin, Thomas Lam, Minh-Tâm Quang Trinh, Nathan Williams. 2022-07-30. Rational Noncrossing Coxeter-Catalan Combinatorics. https://arxiv.org/abs/2208.00121

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