Geodesic
EL-Shellability of Generalized Noncrossing Partitions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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In this article we prove that the poset of m-divisible noncrossing partitions is EL-shellable for every well-generated complex reflection group. This was an open problem for type G(d,d,n) and for the exceptional types, for which a proof is given case-by-case. 
@article{DMTCS_2012_special_263_a46,
     author = {M\"uhle, Henri},
     title = {EL-Shellability of {Generalized} {Noncrossing} {Partitions}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3060/}
}
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Mühle, Henri. EL-Shellability of Generalized Noncrossing Partitions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3060. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3060/

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