Abstract
In this paper we study the partially ordered set of the involutions of the symmetric group S n with the order induced by the Bruhat order of S n. 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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Incitti, F. The Bruhat Order on the Involutions of the Symmetric Group. Journal of Algebraic Combinatorics 20, 243–261 (2004). https://doi.org/10.1023/B:JACO.0000048514.62391.f4
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DOI: https://doi.org/10.1023/B:JACO.0000048514.62391.f4