Year: 2026
Type: preprint
Abstract: Let $V$ be an $n$-dimensional vector space over the finite field $\mathbb F_q$, where $n\ge 2$. It is classical that $q+1$ proper subspaces are necessary and sufficient to cover $V$. We study extremal refinements of this covering theorem. For $1\le m\le q+1$, we determine the maximum possible size of the union of $m$ proper subspaces of $V$, proving that $$ \max_{W_1,\ldots,W_m
Source: arXiv (Cornell University)
Author: Aliabadi, Mohsen
Institution: Clayton State University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Science Foundation Ireland
OpenAlex ID: W7221039209