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

被引：6

作者：

Athanasiadis, Christos A. ^{[1
]}

Kallipoliti, Myrto ^{[1
]}

机构：

[1] Univ Athens, Dept Math, Div Algebra Geometry, Athens 15784, Greece

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2008年 / 115卷 / 07期

关键词：

symmetric group; partial order; absolute order; Mobius function; constructible complex; Cohen-Macaulay complex;

D O I：

10.1016/j.jcta.2007.12.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：1286 / 1295

页数：10

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