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We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type $D_n$ and those of exceptional type and rank at least three.
Watt, C., Brady, T. & Athanasiadis, C. (2007). Shellability of Noncrossing Partition Lattices. Proceedings of the American Mathematical Society, vol. 135, no. 4, pg. 939--949. doi:10.1090/S0002-9939-06-08534-0