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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Shellability of noncrossing partition lattices


Authors: Christos A. Athanasiadis, Thomas Brady and Colum Watt
Journal: Proc. Amer. Math. Soc. 135 (2007), 939-949
MSC (2000): Primary 20F55; Secondary 05E15, 05E99, 06A07
Published electronically: September 26, 2006
MathSciNet review: 2262893
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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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Additional Information

Christos A. Athanasiadis
Affiliation: Department of Mathematics, University of Crete, 71409 Heraklion, Crete, Greece
Address at time of publication: Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, Greece
Email: caath@math.uoa.gr

Thomas Brady
Affiliation: School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
Email: tom.brady@dcu.ie

Colum Watt
Affiliation: School of Mathematics, Dublin Institute of Technology, Dublin 8, Ireland
Email: colum.watt@dit.ie

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08534-0
PII: S 0002-9939(06)08534-0
Keywords: Noncrossing partitions, real reflection group, partially ordered set, shellability, Coxeter element, reflection ordering
Received by editor(s): August 1, 2005
Received by editor(s) in revised form: October 25, 2005
Published electronically: September 26, 2006
Additional Notes: This work was supported in part by the American Institute of Mathematics (AIM) and the NSF
Communicated by: John R. Stembridge
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.