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- W4320341907 abstract "For a finite point set $P subset mathbb{R}^d$, denote by $text{diam}(P)$ the ratio of the largest to the smallest distances between pairs of points in $P$. Let $c_{d, alpha}(n)$ be the largest integer $c$ such that any $n$-point set $P subset mathbb{R}^d$ in general position, satisfying $text{diam}(P) < alphasqrt[d]{n}$, contains an $c$-point convex independent subset. We determine the asymptotics of $c_{d, alpha}(n)$ as $n to infty$ by showing the existence of positive constants $beta = beta(d, alpha)$ and $gamma = gamma(d)$ such that $beta n^{frac{d-1}{d+1}} le c_{d, alpha}(n) le gamma n^{frac{d-1}{d+1}}$ for $alphageq 2$." @default.
- W4320341907 created "2023-02-13" @default.
- W4320341907 creator A5062840017 @default.
- W4320341907 creator A5081837140 @default.
- W4320341907 date "2022-04-05" @default.
- W4320341907 modified "2023-09-23" @default.
- W4320341907 title "Convex polytopes in restricted point sets in $mathbb{R}^d$" @default.
- W4320341907 doi "https://doi.org/10.48550/arxiv.2204.02487" @default.
- W4320341907 hasPublicationYear "2022" @default.
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