The Bruhat Order of the Symmetric Group is Lexicographically Shellable
نویسندگان
چکیده
منابع مشابه
The Bruhat Order on the Involutions of the Symmetric Group
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.
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Let In be the set of involutions in the symmetric group Sn, and for A ⊆ {0, 1, . . . , n}, let F n = {σ ∈ In | σ has a fixed points for some a ∈ A}. We give a complete characterisation of the sets A for which F n , with the order induced by the Bruhat order on Sn, is a graded poset. In particular, we prove that F {1} n (i.e., the set of involutions with exactly one fixed point) is graded, which...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1981
ISSN: 0002-9939
DOI: 10.2307/2043939