Large k-D Simplices in the d-Dimensional Cube
نویسندگان
چکیده
منابع مشابه
Distributions of Points in d Dimensions and Large k - Point Simplices ( Extended Abstract )
We consider a variant of Heilbronn’s triangle problem by asking for fixed dimension d ≥ 2 and for fixed integers k ≥ 3 with k ≤ d+ 1 for a distribution of n points in the d-dimensional unit-cube [0, 1] such that the minimum volume of a k-point simplex among these n points is as large as possible. Denoting by ∆k,d(n) the supremum of the minimum volume of a k-point simplex among n points over all...
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We consider a variant of Heilbronn’s triangle problem by investigating for fixed dimension d ≥ 2 and for integers k ≥ 2 with k ≤ d distributions of n points in the d-dimensional unit cube [0, 1] such that the minimum volume of the simplices, which are determined by (k+1) of these n points, is as large as possible. Denoting by ∆k,d(n) the supremum of the minimum volume of a (k+1)-point simplex a...
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