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Discrete & Computational Geometry
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We prove that a (k−1)-separated family of n compact convex sets in Rd can be met byk-transversals in at mostOdd22k+1-2knk+1kd-k or, for fixed k and d, O(nk(k+1)(d−k)) different order types. This is the first non-trivial bound for 1kd−1.