Summary: Journal of Combinatorial Theory, Series A 115 (2008) 1286­1295
www.elsevier.com/locate/jcta
Note
The absolute order on the symmetric group,
constructible partially ordered sets
and Cohen­Macaulay complexes
Christos A. Athanasiadis 1
, Myrto Kallipoliti
Department of Mathematics (Division of Algebra­Geometry), University of Athens, Panepistimioupolis,
15784 Athens, Greece
Received 12 June 2007
Available online 20 February 2008
Abstract
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 Cohen­Macaulay. 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.

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

Collections: Mathematics