JOURNAL ARTICLE

Rational noncrossing Coxeter–Catalan combinatorics.

  • Published In: Proceedings of the London Mathematical Society, 2024, v. 129, n. 4. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Galashin, Pavel; Lam, Thomas; Trinh, Minh‐Tâm; Williams, Nathan 3 of 3

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. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Proceedings of the London Mathematical Society. 2024/10, Vol. 129, Issue 4, p1
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2024
  • ISSN:0024-6115
  • DOI:10.1112/plms.12643
  • Accession Number:180170602
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