  We give a new description of the Pieri rule for k-Schur functions using the
Bruhat order on the affine type-A Weyl group. In doing so, we prove a new
combinatorial formula for representatives of the Schubert classes for the
cohomology of affine Grassmannians. We show how new combinatorics involved in
our formulas gives the Kostka-Foulkes polynomials and discuss how this can be
applied to study the transition matrices between Hall-Littlewood and k-Schur
functions.
