 
Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 135, Number 4, April 2007, Pages 939949
S 00029939(06)085340
Article electronically published on September 26, 2006
SHELLABILITY OF NONCROSSING PARTITION LATTICES
CHRISTOS A. ATHANASIADIS, THOMAS BRADY, AND COLUM WATT
(Communicated by John R. Stembridge)
Abstract. We give a casefree proof that the lattice of noncrossing partitions
associated to any finite real reflection group is ELshellable. Shellability of
these lattices was open for the groups of type Dn and those of exceptional
type and rank at least three.
1. Introduction
Consider a finite real reflection group W and the partial order on W defined by
letting u v if there exists a shortest factorization of u as a product of reflections
in W which is a prefix of such a shortest factorization of v. This order turns W into
a graded poset having the identity 1 as its unique minimal element. For a Coxeter
element of W, viewed as a finite Coxeter group, we denote by NCW () the interval
[1, ] in this partial order. Since all Coxeter elements of W are conjugate to each
other, the isomorphism type of the poset NCW () is independent of . We denote
