  In this paper we prove instances of the cyclic sieving phenomenon for finite
Grassmannians and partial flag varieties, which carry the action of various
tori in the finite general linear group GL_n(F_q). The polynomials involved are
sums of certain weights of the minimal length parabolic coset representatives
of the symmetric group S_n, where the weight of a coset representative can be
written as a product over its inversions.
