A note on the unstability conditions of the Steenrod squares on the polynomial algebra

Let P(n) = F2[x1, x2, . . . , xn] be the polynomial algebra at the prime 2 in the variables x1, x2, . . . , xn of grading 1. It is a graded module over the Steenrod algebra. In this paper the author presents some useful tools to compute the action of the Steenrod squares on P(n) and applies them to deduce some hit monomials from the others. Then he introduces particular matrices, called “Sq-matrices”, and shows how they can be used to compute the Steenrod squares on P(2).