THE ADMISSIBLE MONOMIAL BASIS FOR THE POLYNOMIAL ALGEBRA OF FIVE VARIABLES IN DEGREE 2s+1 + 2s − 5

Abstract

Let Pk := F2[x1, x2,...,xk] be the polynomial algebra over the prime

field of two elements, F2, in k variables x1, x2,...,xk, each of degree 1.

We study the hit problem, set up by F. Peterson, of finding a minimal set

of generators for Pk as a module over the mod-2 Steenrod algebra, A. In

this paper, we explicitly determine all admissible monomials for the case

k = 5 in degree 2s+1 + 2s − 5 with s an arbitrary positive integer.