The hit problem for the polynomial algebra in some weight vectors

Let P-k := F-2[X-1, X-2, ..., X-k] be the polynomial algebra over the prime field of two elements, F-2, ink variables x(1), x(2), ..., x(k), each of degree 1. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for P-k as a module over the mod-2 Steenrod algebra. In this paper, we extend a result in [12] on the hit problem in degree (k - 1)(2(d) - 1) with k >= 6, by explicitly computing the hit problem in some weight vectors of degree k - 1. (C) 2020 Elsevier B.V. All rights reserved.