Sphere-and-point incidence relations in high dimensions with applications to unit distances and furthest-neighbor pairs (Q1113458)
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scientific article; zbMATH DE number 4082401
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sphere-and-point incidence relations in high dimensions with applications to unit distances and furthest-neighbor pairs |
scientific article; zbMATH DE number 4082401 |
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Sphere-and-point incidence relations in high dimensions with applications to unit distances and furthest-neighbor pairs (English)
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1989
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The paper gives an upper bound for the number of incidences in d- dimensional euclidean space between n points and spheres which are subject to certain conditions on their positions. Similar results for points and lines respectively points and circles in an euclidean plane are due to \textit{E. Szemerédi} and \textit{W. T. Trotter jun.} [Combinatorica 3, 381-392 (1983; Zbl 0541.05012)] and \textit{J. Beck} [Combinatorica 3, 281-297 (1983; Zbl 0533.52004)], respectively. In addition the author discusses the number of unit distances and furtherst- neighbor pairs among n points in d-dimensional euclidean space.
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sphere-point
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incidence
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unit distances
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furthest neighbor points
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