THE ADMISSIBLE MONOMIAL BASIS FOR THE POLYNOMIAL ALGEBRA IN DEGREE THIRTEEN

Abstract

Let P(n)=F2[x1,x2,...,xn] be the polynomial algebra in n variables xi, of degree one, over the field F2 of two elements. The mod-2 Steenrod algebra A acts on P(n) according to well known rules. The hit problem, set up by F.Peterson, of determiningA+P(n), the subspace of all polynomials in the image of the action of the mod-2 Steenrod algebra has been studied by several authors. We are interested in the related problem of determining a basis for the quotient vector space Q(n)=P(n)/A+P(n). In this paper, we give an explicit formula for the dimension of Q(n) in degree thirteen.