POINTS SURROUNDING THE ORIGIN

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Suppose d > 2, n > d+ 1, and we have a set P of n points in d-dimensional Euclidean space. Then P contains a subset Q of d points such that for any p is an element of P, the convex hull of QU{p} does not contain the origin in its interior. We also show that for non-empty, finite point sets A(1),...,A(d+1) in R(d) if the origin is contained in the convex hull of A(i)UA(j) for all 1 <= i < j <= d+1, then there is a simplex S containing the origin such that vertical bar S boolean AND A(i)vertical bar=1 for every 1 < i <= d+1. This is a generalization of Barany's colored Caratheodory theorem, and in a dual version, it gives a spherical version of Lovasz' colored Helly theorem.
Publisher
SPRINGER
Issue Date
2008
Language
English
Article Type
Article
Keywords

K-SETS; THEOREM

Citation

COMBINATORICA, v.28, no.6, pp.633 - 644

ISSN
0209-9683
DOI
10.1007/s00493-008-2427-5
URI
http://hdl.handle.net/10203/89880
Appears in Collection
MA-Journal Papers(저널논문)
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