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Abstract: The midpoint set MS of a set S of points is the set of all midpoints ofpairs of points in S. We study the largest cardinality of a midpoint set MSin a finite-dimensional normed space, such that MS is contained in the unitsphere, and S is outside the closed unit ball. We show in three dimensions thatthis maximum if it exists is determined by the facial structure of the unitball. In higher dimensions no such relationship exists. We also determine themaximum for euclidean and sup norm spaces.



Author: Konrad J. Swanepoel

Source: https://arxiv.org/



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