Classification of seven-point four-distance sets in the plane (Q351648)
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scientific article; zbMATH DE number 6185227
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classification of seven-point four-distance sets in the plane |
scientific article; zbMATH DE number 6185227 |
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Classification of seven-point four-distance sets in the plane (English)
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8 July 2013
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A point set \(X\) in the Euclidean plane is called a \(k\)-distance set if there are exactly \(k\) different distances between two distinct points in \(X.\) Two planar sets are called isomorphic if there exists a similar transformation from one to the other. The main result of the paper states that there are only \(42\) seven-point four distance sets in the plane up to isomorphism. All these sets are shown in a figure.
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\(n\)-point \(k\)-distance set
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isomorphism
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diameter graph
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0.8875954
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0.87033916
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0.8695132
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0.84836036
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0.83798504
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0.83771694
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0.83431435
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