论文信息 - The number of extreme pairs of finite point-sets in Euclidean spaces

The number of extreme pairs of finite point-sets in Euclidean spaces

Abstract To points p and q of a finite set S in d-dimensional Euclidean space Ed are extreme if {p, q} = S ∩ h, for some open halfspace h. Let e2(d)(n) be the maximum number of extreme pairs realized by any n points in Ed. We give geometric proofs of e 2 (2) (n) = ⌊ 3n 2 ⌋ , if n⩾4, and e2(3)(n) = 3n−6, if n⩾6. These results settle the question since all other cases are trivial.

Herbert Edelsbrunner | Gerd Stöckl

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