翻訳と辞書 Words near each other ・ Associação das Escolas de Samba da Cidade do Rio de Janeiro ・ Associação de Basquete Cearense ・ Associação de Educação Física e Desportiva ・ Associação de Escuteiros de Angola ・ Associação de Jovens da Fonte do Bastardo ・ Associação de Paula e Montecristo Voleibol ・ Associação Desportiva Atlética do Paraná ・ Associação Desportiva Bahia de Feira ・ Associação Desportiva Brusque ・ Association québécoise de linguistique ・ Association Reset-Dialogues on Civilizations ・ Association Residence Nursing Home ・ Association Royale des Radio Amateurs du Maroc ・ Association rule learning ・ Association Salé ・ Association scheme ・ Association Scientifique Internationale pour le Café ・ Association Scoute du Togo ・ Association Solidarité Féminine ・ Association Sonneurs de Veuzes ・ Association Sportive Achbal Ismailia Meknés ・ Association Sportive d'Hammamet H.C. ・ Association Sportive de Bamako ・ Association Sportive Niamey ・ Association Sportive Oussou Saka ・ Association Sportive Tadjourah ・ Association Sportive Ville Blida ・ Association theory ・ Association to Advance Collegiate Schools of Business ・ Association to Safeguard Giraffes in Niger Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Association scheme ： ウィキペディア英語版 Association scheme The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance. In mathematics, association schemes belong to both algebra and combinatorics. Indeed, in algebraic combinatorics, association schemes provide a unified approach to many topics, for example combinatorial designs and coding theory. In algebra, association schemes generalize groups, and the theory of association schemes generalizes the character theory of linear representations of groups. ==Definition== An n-class association scheme consists of a set ''X'' together with a partition ''S'' of ''X'' × ''X'' into n + 1 binary relations, R0, R1, ..., Rn which satisfy: *$R\_=\backslash$ and is called the Identity relation. *Defining $R^$ * :=\, if ''R'' in ''S'', then ''R *'' in ''S'' *If $(x,y)\backslash in\; R\_$, the number of $z\backslash in\; X$ such that $(x,z)\backslash in\; R\_$ and $(z,y)\backslash in\; R\_$ is a constant $p^k\_$ depending on $i$, $j$, $k$ but not on the particular choice of $x$ and $y$. An association scheme is ''commutative'' if $p\_^k=p\_^k$ for all $i$, $j$ and $k$. Most authors assume this property. A ''symmetric'' association scheme is one in which each relation $R\_i$ is a symmetric relation. That is: * if (''x'',''y'') ∈ ''R''''i'', then (''y'',''x'') ∈ ''R''''i'' . (Or equivalently, ''R'' * = ''R''.) Every symmetric association scheme is commutative. Note, however, that while the notion of an association scheme generalizes the notion of a group, the notion of a commutative association scheme only generalizes the notion of a commutative group. Two points ''x'' and ''y'' are called ''i'' th associates if $(x,y)\backslash in\; R\_$. The definition states that if ''x'' and ''y'' are ''i'' th associates so are ''y'' and ''x''. Every pair of points are ''i'' th associates for exactly one $i$. Each point is its own zeroth associate while distinct points are never zeroth associates. If ''x'' and ''y'' are ''k'' th associates then the number of points $z$ which are both ''i'' th associates of $x$ and ''j'' th associates of $y$ is a constant $p^k\_$. 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「Association scheme」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.