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Paper detail

Rational Noncrossing Coxeter-Catalan Combinatorics

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.

preprint2022arXivOpen access
Pavel GalashinThomas LamMinh-Tâm Quang TrinhNathan Williams
math.COmath.RT
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Pavel GalashinThomas LamMinh-Tâm Quang TrinhNathan Williams

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