J. Pach

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19962026

most citedErdos-Szekeres-type theorems for monotone paths and convex bodies

48 citations · 165 across the 65 of their papers we have counts for

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Showing 1996 · math.MGShow all

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math.MG1996

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

János Pach, Joel Spencer

Let $d_{1} \leq d_{2} \leq \dots \leq d_{(2 n)}$ 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 mini…