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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 Beck–Fiala theorem ： ウィキペディア英語版 Beck–Fiala theorem In mathematics, the Beck–Fiala theorem is a major theorem in discrepancy theory due to József Beck and Tibor Fiala. Discrepancy is concerned with coloring elements of a ground set such that each set in a certain set system is as balanced as possible, i.e., has approximately the same number of elements of each color. The Beck–Fiala theorem is concerned with the case where each element doesn't appear many times across all sets. The theorem guarantees that if each element appears at most ''t'', then the elements can be colored so that the imbalance is bounded by 2''t'' − 1. ==Statement== Formally, given a universe : $()\; =\; \backslash$ and a collection of subsets : $S\_1,\; S\_2,\; \backslash ldots,\; S\_m\; \backslash subseteq\; ()$ such that for each $i\; \backslash in\; ()$, : $\backslash vert\; \backslash \; \backslash vert\; \backslash leq\; t,$ then one can find an assignment of : $x\; :\; ()\; \backslash rightarrow\; \backslash$ such that : $x(S\_j)\; \backslash leq\; 2t-1,\; \backslash forall\; j\; \backslash textx(S\_j)\; :=\; \backslash sum\_\; x\_i.$ 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「Beck–Fiala 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.