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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 Folkman's theorem ： ウィキペディア英語版 Folkman's theorem Folkman's theorem is a theorem in mathematics, and more particularly in arithmetic combinatorics and Ramsey theory. According to this theorem, whenever the natural numbers are partitioned into finitely many subsets, there exist arbitrarily large sets of numbers all of whose sums belong to the same subset of the partition.〔.〕 The theorem had been discovered and proved independently by several mathematicians,〔.〕〔.〕 before it was named "Folkman's theorem", as a memorial to Jon Folkman, by Graham, Rothschild, and Spencer.〔 ==Statement of the theorem== Let N be the set of positive integers, and suppose that N is partitioned into ''k'' different subsets ''N''1, ''N''2, ... ''N''''k'', where ''k'' is any positive integer. Then Folkman's theorem states that, for every positive integer ''m'', there exists a set ''S''''m'' and an index ''i''''m'' such that ''S''''m'' has ''m'' elements and such that every sum of a nonempty subset of ''S''''m'' belongs to ''N''''i''''m''.〔 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「Folkman'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.