On the Peterson hit problem

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 study a minimal set of generators for A-module Pk in some so-called generic degrees and apply these results to explicitly determine the hit problem for k=4.