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

Abstract

Let Pk := F2[x1,x2,...,xk] be the polynomial algebra over the prime field of two elements, F2, ink 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 2 s+1 +2 s −5 withs an arbitrary positive integer.