Nguyen Sum

## On the hit problem for the polynomial algebra

slide: PDF.
video: comming soon.
abstract:
We study the problem of determining a minimal set of generators for the polynomial algebra $$P_k := \mathbb{F}_2[x_1,x_2,\ldots,x_k]$$ as a module over the mod-2 Steenrod algebra, $$\mathcal{A}$$. In this paper, we study a minimal set of generators for $$\mathcal{A}$$-module $$P_k$$ in some so-call generic degrees and apply these results to explicitly determine the hit problem for $$k=4$$.