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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 Kneser's theorem (combinatorics) ： ウィキペディア英語版 Kneser's theorem (combinatorics) In mathematics, Kneser's theorem is an inequality among the sizes of certain sumsets in finite abelian groups. It belongs to the field of additive combinatorics, and is named after Martin Kneser, who published it in 1953.〔 〕 It may be regarded as an extension of the Cauchy–Davenport theorem, which also concerns sumsets in groups but is restricted to groups whose order is a prime number.〔Geroldinger & Rusza (2009) p.143〕 ==Statement== Let ''G'' be a non-trivial abelian group and ''A'', ''B'' finite non-empty subsets. If |''A''| + |''B''| ≤ |''G''| then there is a finite subgroup ''H'' of ''G'' such that : The subgroup ''H'' can be taken to be the ''stabiliser''〔 of ''A''+''B'' :$H\; =\; \backslash lbrace\; g\; \backslash in\; G\; :\; g\; +\; (A+B)\; =\; (A+B)\; \backslash rbrace.$ 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「Kneser's theorem (combinatorics)」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.