Shellability of noncrossing partition lattices

Athanasiadis, Christos; Brady, Thomas; Watt, Colum

doi:10.1090/S0002-9939-06-08534-0

Shellability of noncrossing partition lattices
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by Christos A. Athanasiadis, Thomas Brady and Colum Watt

Proc. Amer. Math. Soc. 135 (2007), 939-949

DOI: https://doi.org/10.1090/S0002-9939-06-08534-0

Published electronically: September 26, 2006

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Abstract:

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.

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