Counting chains in the noncrossing partition lattice via the W-Laplacian
نویسندگان
چکیده
We give an elementary, case-free, Coxeter-theoretic derivation of the formula hnn!/|W| for number maximal chains in noncrossing partition lattice NC(W) a real reflection group W. Our proof proceeds by comparing Deligne-Reading recursion with parabolic characteristic polynomial W-Laplacian matrix considered our previous work. further discuss consequences this geometric theory spherical and affine Artin groups.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2022
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2022.02.023