The Bruhat Order on the Involutions of the Symmetric Group
The Bruhat Order on the Involutions of the Symmetric Group
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对称群对合的 Bruhat 阶
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
F. Incitti
中科院分区：
文献类型：
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作者：
F. Incitti
本文研究了对称群Sn的对合的偏序集，其阶由Sn的Bruhat阶导出。我们证明了这是一个分次偏序集，秩函数由反演数和超越数的平均数给出，并且它是字典序可壳的，因此是Cohen-Macaulay和Eulerian的。
In this paper we study the partially ordered set of the involutions of the symmetric group Sn with the order induced by the Bruhat order of Sn. We prove that this is a graded poset, with rank function given by the average of the number of inversions and the number of excedances, and that it is lexicographically shellable, hence Cohen-Macaulay, and Eulerian.