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arXiv · 2609.32475

On the hit problem of rank five

Nguyen Sum
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Abstract

Let $P_q$ be the graded polynomial algebra $\mathbb F_2[x_1,x_2,\ldots ,x_q]$ over the prime field of two elements, $\mathbb F_2$, with the degree of each $x_i$ being 1. We study the {\it hit Peterson problem} of finding a minimal set of generators for $P_q$ as a module over the mod-$2$ Steenrod algebra, $\mathcal{A}.$ In this note, we present the minimal sets of $\mathcal{A}$-generators for $P_5$ in the cases where the degree are sufficiently general.

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Nguyen Sum. 2026-09-26. On the hit problem of rank five. https://arxiv.org/abs/2609.32475

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