Journal of Algebraic Combinatorics

, Volume 20, Issue 3, pp 243–261

The Bruhat Order on the Involutions of the Symmetric Group

  • Federico Incitti

DOI: 10.1023/B:JACO.0000048514.62391.f4

Cite this article as:
Incitti, F. Journal of Algebraic Combinatorics (2004) 20: 243. doi:10.1023/B:JACO.0000048514.62391.f4


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.

symmetric groupBruhat orderinvolutionEL-shellabilityCohen-Macaulay

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Federico Incitti
    • 1
  1. 1.Dipartimento di MatematicaUniversità “La Sapienza”Italy