The absolute order on the symmetric group, constructible partially ordered sets and Cohen-Macaulay complexes |
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Authors: | Christos A. Athanasiadis Myrto Kallipoliti |
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Affiliation: | Department of Mathematics (Division of Algebra-Geometry), University of Athens, Panepistimioupolis, 15784 Athens, Greece |
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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. |
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Keywords: | Symmetric group Partial order Absolute order Mö bius function Constructible complex Cohen-Macaulay complex |
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