  One constructs minimal injective resolutions for certain unstable modules
that appears to be the mod 2 cohomology of Thom spectra. The terms of the
resolution are tensor products of Brown-Gitler modules and Steinberg modules
introduced by S. Mitchell and S. Priddy. A combinatorial result of Andrews
shows that the alternating sum of the Poincare series of the considered modules
is zero. One gives homotopical applications of this result.
