2022/07/30 by Pavel Galashin, Galashin, Pavel, Thomas Lam +5 · 1 citation
Computer Science · Materials Science · Mathematics · #05E10 #20C08 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Primary: 05A15. Secondary: 05E05 #Quasicrystal Structures and Properties #Representation Theory (math.RT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2208.00121
openalex publication_date 2022/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.