On Extensive Subsets of Convex Bodies |
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Authors: | Talata István |
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Institution: | (1) Department of Mathematics, Auburn University, 218 Parker Hall, Auburn, AL 36849-5310, USA |
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Abstract: | A subset S of a d-dimensional convex body K is extensive if S
∂K and for any p, q ∈ S the distance between p and q is at least one-half of the maximum length of chords of K parallel to the segment pq. In this paper we establish the general upper bound |S| ≤ 3
d
— 1. We also find an upper bound for a certain class of 3-polytopes, which leads to the determination of the maximum cardinalities
of extensive subsets and their extremal configurations for tetrahedra, octahedra and some other 3-polytopes.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | 52C17 (52B10) 3-dimensional polytope antipodality kissing number Minkowski metric translative packing |
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