 Serre polynomial generators for mod-two Eilenberg–MacLane cohomology

For $n\ge 1$, the mod-two cohomology of $K(\mathbb{Z}/2,n)$ is polynomial on the admissible operations in the displayed strict-excess range, including the empty operation. It is obtained from path-space transgressions and compatibility with Steenrod squares. Products must still be included when listing low-degree vector-space bases.