翻訳と辞書 Words near each other ・ Erdély TV ・ Erdélyi ・ Erdélyi Bastion ・ Erdélyi Napló ・ Erdöl-Erdgas-Museum Twist ・ Erdös-Rényi Prize in Network Science ・ Erdőbénye ・ Erdőfalva ・ Erdőhorváti ・ Erdőkertes ・ Erdőkürt ・ Erdős ・ Erdős arcsine law ・ Erdős cardinal ・ Erdős conjecture on arithmetic progressions ・ Erdős distinct distances problem ・ Erdős number ・ Erdős Prize ・ Erdős space ・ Erdősmecske ・ Erdősmárok ・ Erdős–Anning theorem ・ Erdős–Bacon number ・ Erdős–Borwein constant ・ Erdős–Burr conjecture ・ Erdős–Diophantine graph ・ Erdős–Faber–Lovász conjecture ・ Erdős–Fuchs theorem ・ Erdős–Gallai theorem ・ Erdős–Graham problem Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Erdős distinct distances problem ： ウィキペディア英語版 Erdős distinct distances problem In discrete geometry, the Erdős distinct distances problem states that between distinct points on a plane there are at least distinct distances. It was posed by Paul Erdős in 1946. In a 2010 preprint, Larry Guth and Nets Hawk Katz announced a solution.〔. See also (The Guth-Katz bound on the Erdős distance problem ) by Terry Tao and (Guth and Katz’s Solution of Erdős’s Distinct Distances Problem ) by János Pach.〕 ==The conjecture== In what follows let denote the minimal number of distinct distances between points in the plane. In his 1946 paper, Erdős proved the estimates $\backslash sqrt-1/2\backslash leq\; g(n)\backslash leq\; c\; n/\backslash sqrt$ for some constant $c$. The lower bound was given by an easy argument, the upper bound is given by a $\backslash sqrt\backslash times\backslash sqrt$ square grid (as there are $O(\; n/\backslash sqrt)$ numbers below ''n'' which are sums of two squares, see Landau–Ramanujan constant). Erdős conjectured that the upper bound was closer to the true value of ''g''(''n''), specifically, $g(n)\; =\; \backslash Omega(n^c)$ holds for every . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Erdős distinct distances problem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.