On the action of Steenrod squares on polynomial algebras II Original Research Article

Let image(2) be the mod-2 Steenrod algebra, and let image] be the mod-2 cohomology of the s-fold product of image with itself, with its usual structure as an image(2)-module. A polynomial image is said to be hit if it is in the image of the action image, wher image is the augmentation ideal of image(2). In this paper we state two equivalent forms of a conjecture that a certain family of monomials is hit, and prove the conjecture in a special case. In the process, we use information about the canonical antiautomorphism χ of image(2) to show that a hit polynomial P remains hit when multiplied by any polynomial raised to a sufficiently high 2-power. The relevant 2-power depends only on the Milnor basis elements required to hit P.