Abstract: N. Bergeron and F. Sottile defined the universal Grassmannian
order on the symmetric group in an attempt to better understand the
Littlewood Richardson coefficients for Schubert polynomials. In this talk,
we will give an alternative characterization of this order in terms of basic
permutation statistics, and use this characterization to establish some
properties of this partial order. In addition, we give a third
characterization of this order that naturally generalizes to define a whole
class of partial orders on the symmetric group.