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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kemnitz's conjecture ： ウィキペディア英語版 Kemnitz's conjecture In additive number theory, Kemnitz's conjecture states that every set of lattice points in the plane has a large subset whose centroid is also a lattice point. It was proved independently in the autumn of 2003 by Christian Reiher and Carlos di Fiore. The exact formulation of this conjecture is as follows: :Let $n$ be a natural number and $S$ a set of 4''n'' − 3 lattice points in plane. Then there exists a subset $S\_1\; \backslash subseteq\; S$ with $n$ points such that the centroid of all points from $S\_1$ is also a lattice point. Kemnitz's conjecture was formulated in 1983 by Arnfried Kemnitz as a generalization of the Erdős–Ginzburg–Ziv theorem, an analogous one-dimensional result stating that every 2''n'' − 1 integers have a subset of size ''n'' whose average is an integer. In 2000, Lajos Rónyai proved a weakened form of Kemnitz's conjecture for sets with 4''n'' − 2 lattice points. Then, in 2003, Christian Reiher proved the full conjecture using the Chevalley–Warning theorem. ==References== * * * * * * 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「Kemnitz's conjecture」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.