Admissible sequence of Steenrod squares ($i_j\ge 2i_{j+1}$)

An index sequence obeying the displayed inequalities represents an admissible product ${\mathrm{Sq}}^{i_1}\cdots {\mathrm{Sq}}^{i_r}$. Its degree increment is the sum of the indices. The Adem relations rewrite every square monomial in terms of admissible ones, whose Steenrod excess controls universal instability.

The excess measures the minimum degree on which an admissible Steenrod monomial can be nonzero. Strict excess below $n$ picks out polynomial generators in the mod-two cohomology of $K(\mathbb{Z}/2,n)$; equality can correspond to a square, rather than a new generator.