Name
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]d such that the minimum volume of a k-point simplex among these n points is as large as possible. Denoting by Δk,d(n) the supremum of the minimum volume of a k-point simplex among n points over all distributions of n points in [0,1]d we will show that ck . (log n)1/( d−−k+2)/n(k−−1)/(d−−k+2) ≤ Δk,d(n) ≤ ck′/n(k−−1)/d for 3 ≤ k ≤ d +1, and moreover Δk,d(n) ≤ ck′′/n(k−−1)/d+(k−−2)/(2d(d−−1)) for k ≥ 4 even, and constants ck, ck′, ck′′ 0. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1007/s00454-007-9041-y | Discrete and Computational Geometry |
Keywords | Field | DocType |
large k-point simplices,minimum volume,odd integers k,n k,n point,d-dimensional unit cube,heilbronn's triangle problem · hypergraphs · independence number,fixed dimension,c k,integers k,triangle problem | Integer,Discrete mathematics,Independence number,Combinatorics,Infimum and supremum,Simplex,Mathematics | Journal |
Volume | Issue | ISSN |
40 | 3 | 0179-5376 |
ISBN | Citations | PageRank |
3-540-28061-8 | 4 | 0.46 |
References | Authors | |
15 | 1 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hanno Lefmann | 1 | 484 | 94.24 |