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 determining A+P(n), the subspace of all polyno

mials 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.