The Bruhat order of the symmetric group
Richard P. Stanley
Department of Mathematics 2-375
Massachusetts Institute of Technology
Cambridge, MA 02139-4307
USA
Abstract Full Text PDF
The Bruhat order of the symmetric group
is a partial ordering of originally described by Ehresmann in order to determine the
relationship among the cells of the Bruhat decomposition of the
complete flag variety. We will discuss some basic properties of this
partial order, including the work of Ehresmann, topological results of
Verma and Björner-Wachs, the determination of the MacNeille
completion by Lascoux-Schützenberger, and recent work by Postnikov
and the speaker on enumerative properties of the Bruhat order related
to Schubert polynomials and Schubert varieties.
