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arXiv · 2607.05767

Universal Cycles for Affine Planes and 3-Subspaces over Finite Fields

Yu Hsuan Hsieh·Ming-Hsuan Kang
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Abstract

We construct universal cycles for affine planes in $\mathbb F_q^n$ for all prime powers $q$ and all $n\ge4$, using sliding windows of length three. The construction is local-to-global: explicit local cycles are built on frame configurations, the linear $2$-subspaces are organized by a layered frame decomposition, and the resulting cycles are assembled by gluing along shared directions. The universal cycle obtained has direction set containing all $1$-subspaces. We also extend the construction to universal cycles for $3$-subspaces of $\mathbb F_q^n$.

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Yu Hsuan Hsieh, Ming-Hsuan Kang. 2026-07-07. Universal Cycles for Affine Planes and 3-Subspaces over Finite Fields. https://arxiv.org/abs/2607.05767

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