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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 Freiman's theorem ： ウィキペディア英語版 Freiman's theorem In mathematics, Freiman's theorem is a combinatorial result in additive number theory. In a sense it accounts for the approximate structure of sets of integers that contain a high proportion of their internal sums, taken two at a time. The formal statement is: Let ''A'' be a finite set of integers such that the sumset :$A\; +\; A\backslash ,$ is small, in the sense that : for some constant $c$. There exists an ''n''-dimensional arithmetic progression of length :$c\text{'}\; |A|\backslash ,$ that contains ''A'', and such that ''c and ''n'' depend only on ''c''.〔Nathanson (1996) p.251〕 A simple instructive case is the following. We always have :$|A\; +\; A|\; \backslash ge\; 2|A|-1$ with equality precisely when ''A'' is an arithmetic progression. This result is due to Gregory Freiman (1964,1966).〔Nathanson (1996) p.252〕 Much interest in it, and applications, stemmed from a new proof by Imre Z. Ruzsa (1994). ==See also== *Markov spectrum 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「Freiman's theorem」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.