# 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}
}```
• Published 2007
• Mathematics
• Transactions of the American Mathematical Society
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
24 Citations

#### References

SHOWING 1-10 OF 53 REFERENCES
Noncrossing Partitions for the Group Dn
• Computer Science, Mathematics
• SIAM J. Discret. Math.
• 2004
• 87
• PDF
Polygon dissections and some generalizations of cluster complexes
• E. Tzanaki
• Mathematics, Computer Science
• J. Comb. Theory, Ser. A
• 2006
• 29
• PDF
Enumeration of m-Ary Cacti
• Mathematics, Computer Science