About: K-set (geometry)

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In discrete geometry, a -set of a finite point set in the Euclidean plane is a subset of elements of that can be strictly separated from the remaining points by a line. More generally, in Euclidean space of higher dimensions, a -set of a finite point set is a subset of elements that can be separated from the remaining points by a hyperplane. In particular, when (where is the size of ), the line or hyperplane that separates a -set from the rest of is a halving line or halving plane.

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  • In discrete geometry, a -set of a finite point set in the Euclidean plane is a subset of elements of that can be strictly separated from the remaining points by a line. More generally, in Euclidean space of higher dimensions, a -set of a finite point set is a subset of elements that can be separated from the remaining points by a hyperplane. In particular, when (where is the size of ), the line or hyperplane that separates a -set from the rest of is a halving line or halving plane. The -sets of a set of points in the plane are related by projective duality to the -levels in an arrangement of lines. The -level in an arrangement of lines in the plane is the curve consisting of the points that lie on one of the lines and have exactly lines below them. Discrete and computational geometers have also studied levels in arrangements of more general kinds of curves and surfaces. (en)
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  • In discrete geometry, a -set of a finite point set in the Euclidean plane is a subset of elements of that can be strictly separated from the remaining points by a line. More generally, in Euclidean space of higher dimensions, a -set of a finite point set is a subset of elements that can be separated from the remaining points by a hyperplane. In particular, when (where is the size of ), the line or hyperplane that separates a -set from the rest of is a halving line or halving plane. (en)
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  • K-set (geometry) (en)
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