Lexicographic shellability of the Bruhat-Chevalley order on   fixed-point-free involutions
  The main purpose of this paper is to prove that the Bruhat-Chevalley ordering of the symmetric group when restricted to the fixed-point-free involutions forms an $EL$-shellable poset whose order complex triangulates a ball. Another purpose of this article is to prove that the Deodhar-Srinivasan poset is a proper, graded subposet of the Bruhat-Chevalley poset on fixed-point-free involutions. 
Mahir Bilen Can and Yonah Cherniavsky and Tim Twelbeck
math.CO math.AG math.AT