2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146821We 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.CombinatoricsRepresentation Theory05E20, 20G05text