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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 135, Number 4, April 2007, Pages 939949
S 0002-9939(06)08534-0
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 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 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

  

Source: Athanasiadis, Christos - Department of Mathematics, University of Athens

 

Collections: Mathematics