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

Authors:
Christos A. Athanasiadis;Myrto Kallipoliti
Affiliations:
Department of Mathematics (Division of Algebra--Geometry), University of Athens, Panepistimioupolis, 15784 Athens, Greece;Department of Mathematics (Division of Algebra--Geometry), University of Athens, Panepistimioupolis, 15784 Athens, Greece
Venue:
Journal of Combinatorial Theory Series A
Year:
2008

Citing 2
Cited 2

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The absolute order of a permutation representation of a Coxeter group

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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 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.