Decomposition numbers for finite Coxeter groups and generalised non-crossing partitions

@article{Krattenthaler2007DecompositionNF,
  title={Decomposition numbers for finite Coxeter groups and generalised non-crossing partitions},
  author={C. Krattenthaler and T. Muller},
  journal={Transactions of the American Mathematical Society},
  year={2007},
  volume={362},
  pages={2723-2787}
}
Given a finite irreducible Coxeter group W, a positive integer d, and types T 1 , T 2 ,...,T d (in the sense of the classification of finite Coxeter groups), we compute the number of decompositions c = σ 1 σ 2 ···σ d of a Coxeter element c of W, such that σ i is a Coxeter element in a subgroup of type T i in W, i = 1, 2,..., d, and such that the factorisation is "minimal" in the sense that the sum of the ranks of the T i 's, i = 1,2,..., d, equals the rank of W. For the exceptional types, these… Expand
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