  We study the permutation action of a finite symplectic group of
characteristic 2 on the set of subspaces of its standard module which are
either totally isotropic or else complementary to totally isotropic subspaces
with respect to the alternating form. A general formula is obtained for the
2-rank of the incidence matrix for the inclusion of one-dimensional subspaces
in the distinguished subspaces of a fixed dimension.
