PreprintCC BY 4.0arXiv
On the hit problem of rank five
Abstract
Let Pq be the graded polynomial algebra 𝔽2[x1,x2,… ,xq] over the prime field of two elements, 𝔽2, with the degree of each xi being 1. We study the {\it hit Peterson problem} of finding a minimal set of generators for Pq as a module over the mod-$2$ Steenrod algebra, 𝒜. In this note, we present the minimal sets of 𝒜-generators for P5 in the cases where the degree are sufficiently general.
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BibTeX
@misc{sum2026problem,
title = {{On the hit problem of rank five}},
author = {Nguyen Sum},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32475},
eprint = {2609.32475},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32475},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the hit problem of rank five
AU - Nguyen Sum
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32475
UR - https://arxiv.org/abs/2609.32475
AB - Let P_q be the graded polynomial algebra 𝔽_2[x_1,x_2,… ,x_q] over the prime field of two elements, 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, 𝒜. In this note, we present the minimal sets of 𝒜-generators for P_5 in the cases where the degree are sufficiently general.
ER -