Non-crossing partitions for classical reflection groups

@article{Reiner1997NoncrossingPF,
  title={Non-crossing partitions for classical reflection groups},
  author={Victor Reiner},
  journal={Discrete Mathematics},
  year={1997},
  volume={177},
  pages={195-222}
}
We introduce analogues of the lattice of non-crossing set partitions for the classical reeection groups of type B and D. The type B analogues ((rst considered by Montenegro in a diierent guise) turn out to be as well-behaved as the original non-crossing set partitions, and the type D analogues almost as well-behaved. In both cases, they are EL-labellable ranked lattices with symmetric chain decompo-sitions (self-dual for type B), whose rank-generating functions, zeta polynomials, rank-selected… CONTINUE READING
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