No Helly Theorem for Stabbing Translates by Lines in R 3
نویسندگان
چکیده
منابع مشابه
On stabbing triangles by lines in 3-space
We give an example of a set P of 3n points in R3 such that, for any partition of P into triples, there exists a line stabbing Ω( √ n) of the triangles determined by the triples.
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Let r be a commutative field (finite or infinite) and let P = P(n, r) be the n-dimensional projective space over ZY Then every point x E P can be expressed by n + 1 homogene coordinates x = (x,,..., x,), not all zero and (x0,..., x,) = @x0,..., Ax,) for OflET. By a hypersurface of degree d we simply mean the set of all points x E P with p(x) = 0, where p(x) is a homogenous polynomial of degree ...
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The d-convex sets in a metric space are those subsets which include the metric interval between any two of its elements. Weak modularity is a certain interval property for triples of points. The d-convexity of a discrete weakly modular space X coincides with the geodesic convexity of the graph formed by the two-point intervals in X. The Helly number of such a space X turns out to be the same as...
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ژورنال
عنوان ژورنال: Discrete and Computational Geometry
سال: 2004
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-003-0796-5