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- W4385018354 abstract "Let $mathbb{F}_q^d$ be the $d$-dimensional vector space over the finite field with $q$ elements. For a subset $Esubseteq mathbb{F}_q^d$ and a fixed nonzero $tin mathbb{F}_q$, let $mathcal{H}_t(E)={h_y: yin E}$, where $h_y$ is the indicator function of the set ${xin E: xcdot y=t}$. Two of the authors, with Maxwell Sun, showed in the case $d=3$ that if $|E|geq Cq^{frac{11}{4}}$ and $q$ is sufficiently large, then the VC-dimension of $mathcal{H}_t(E)$ is 3. In this paper, we generalize the result to arbitrary dimension and improve the exponent in the case $d=3$." @default.
- W4385018354 created "2023-07-22" @default.
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- W4385018354 date "2023-07-19" @default.
- W4385018354 modified "2023-10-12" @default.
- W4385018354 title "VC-Dimension of Hyperplanes over Finite Fields" @default.
- W4385018354 doi "https://doi.org/10.48550/arxiv.2307.10425" @default.
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