2020
DOI: 10.19086/da.11949
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Abstract: Let P be a set of n points in real projective d-space, not all contained in a hyperplane, such that any d points span a hyperplane. An ordinary hyperplane of P is a hyperplane containing exactly d points of P. We show that if d 4, the number of ordinaryif n is sufficiently large depending on d. This bound is tight, and given d, we can calculate the exact minimum number for sufficiently large n. This is a consequence of a structure theorem for sets with few ordinary hyperplanes: For any d 4 and K > 0, if n C d … Show more

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