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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 covering system ： ウィキペディア英語版 covering system In mathematics, a covering system (also called a complete residue system) is a collection :$\backslash ),\backslash \; \backslash ldots,\backslash \; a\_k(\backslash mathrm\backslash \; )\backslash \}$ of finitely many residue classes $a\_i(\backslash mathrm\backslash \; )\; =\; \backslash$ whose union contains every integer. == Examples and definitions == The notion of covering system was introduced by Paul Erdős in the early 1930s. The following are examples of covering systems: :$\backslash ),\backslash \; 1(\backslash mathrm\backslash \; ),\backslash \; 2(\backslash mathrm\backslash \; )\backslash \},$ and :$\backslash ),\backslash \; 2(\backslash mathrm\backslash \; ),\backslash \; 4(\backslash mathrm\backslash \; ),\backslash \; 0(\backslash mathrm\backslash \; )\backslash \},$ and :$\backslash ),\backslash \; 0(\backslash mathrm\backslash \; ),\backslash \; 1(\backslash mathrm\backslash \; ),$ \ 5(\mathrm\ ),\ 7(\mathrm\ ) \}. A covering system is called ''disjoint'' (or ''exact'') if no two members overlap. A covering system is called ''distinct'' (or ''incongruent'') if all the moduli $n\_i$ are different (and bigger than 1). A covering system is called ''irredundant'' (or ''minimal'') if all the residue classes are required to cover the integers. The first two examples are disjoint. The third example is distinct. A system (i.e., an unordered multi-set) :$\backslash ),\backslash \; \backslash ldots,\backslash \; a\_k(\backslash mathrm\backslash \; )\backslash \}$ of finitely many residue classes is called an $m$-cover if it covers every integer at least $m$ times, and an ''exact'' $m$-cover if it covers each integer exactly $m$ times. It is known that for each $m=2,3,\backslash ldots$ there are exact $m$-covers which cannot be written as a union of two covers. For example, :$\backslash );\backslash \; 0(\backslash mathrm\backslash \; );\backslash \; 2(\backslash mathrm\backslash \; );\backslash \; 0,4,6,8(\backslash mathrm\backslash \; );$ :$1,2,4,7,10,13(\backslash mathrm\backslash \; );\backslash \; 5,11,12,22,23,29(\backslash mathrm\backslash \; )$ \} is an exact 2-cover which is not a union of two covers. 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「covering system」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.