Uniformly distributed distances: A geometric application of Jansen's inequality

Simple item page
dc.creatorPach, János
dc.creatorSpencer, Joel
dc.date1996-05-10
dc.date.accessioned2026-07-07T09:15:31Z
dc.date.available2026-07-07T09:15:31Z
dc.descriptionLet $d_1\leq d_2\leq\ldots\leq d_{n\choose 2}$ denote the distances determined by $n$ points in the plane. It is shown that $\min\sum_i (d_{i+1}-d_i)^2=O(n^{-6/7})$, where the minimum is taken over all point sets with minimal distance $d_1 \geq 1$. This bound is asymptotically tight.
dc.identifierhttps://arxiv.org/abs/math/9605221
dc.identifierhttp://arxiv.org/abs/math/9605221
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153046
dc.subjectMetric Geometry
dc.titleUniformly distributed distances: A geometric application of Jansen's inequality
dc.typetext

Files

Collections

arXiv