5 research outputs found
The absolute order on the symmetric group, constructible partially ordered sets and Cohen-Macaulay complexes
The absolute order is a natural partial order on a Coxeter group W. It can be
viewed as an analogue of the weak order on W in which the role of the
generating set of simple reflections in W is played by the set of all
reflections in W. By use of a notion of constructibility for partially ordered
sets, it is proved that the absolute order on the symmetric group is homotopy
Cohen-Macaulay. This answers in part a question raised by V. Reiner and the
first author. The Euler characteristic of the order complex of the proper part
of the absolute order on the symmetric group is also computed.Comment: Final version (only minor changes), 10 pages, one figur
The absolute order on the symmetric group, constructible partially ordered sets and Cohen-Macaulay complexes
The absolute order is a natural partial order on a Coxeter group W. It can be viewed as an analogue of the weak order on W in which the role of the generating set of simple reflections in W is played by the set of all reflections in W. By use of a notion of constructibility for partially ordered sets, it is proved that the absolute order on the symmetric group is homotopy Cohen-Macaulay. This answers in part a question raised by V. Reiner and the first author. The Euler characteristic of the order complex of the proper part of the absolute order on the symmetric group is also computed. © 2008 Elsevier Inc. All rights reserved