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Title: Rational noncrossing Coxeter–Catalan combinatorics
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.  more » « less
Award ID(s):
1953852 2246877 2046915 1954121
PAR ID:
10574705
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
London Mathematical Society
Date Published:
Journal Name:
Proceedings of the London Mathematical Society
Volume:
129
Issue:
4
ISSN:
0024-6115
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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