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arXiv:0706.1405 [math.CO]AbstractReferencesReviewsResources

The absolute order on the symmetric group, constructible partially ordered sets and Cohen-Macaulay complexes

Christos A. Athanasiadis, Myrto Kallipoliti

Published 2007-06-11, updated 2008-01-07Version 2

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.

Comments: Final version (only minor changes), 10 pages, one figure
Categories: math.CO
Subjects: 06A11
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