LAUSR

Let Pk be the graded polynomial algebra ????2[x1,x2,…,xk]$\mathbb {F}_{2}[x_{1},x_{2},{\ldots } ,x_{k}]$ over the prime field of two elements, ????2$\mathbb {F}_{2}$, with the degree of each xi being 1. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for Pk as a module over the mod-2 Steenrod algebra, ????$\mathcal {A}$. In this paper, we explicitly determine a minimal set of ????$\mathcal {A}$-generators for Pk in the case k = 5 and the degree 4(2d−1) with d an arbitrary positive integer.