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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 Cremona–Richmond configuration ： ウィキペディア英語版 Cremona–Richmond configuration In mathematics, the Cremona–Richmond configuration is a configuration of 15 lines and 15 points, having 3 points on each line and 3 lines through each point, and containing no triangles. It was studied by and . It is a generalized quadrangle with parameters (2,2). Its Levi graph is the Tutte–Coxeter graph.〔 ==Symmetry== The points of the Cremona–Richmond configuration may be identified with the $15=\backslash binom$ unordered pairs of elements of a six-element set; these pairs are called ''duads''. Similarly, the lines of the configuration may be identified with the 15 ways of partitioning the same six elements into three pairs; these partitions are called ''synthemes''. Identified in this way, a point of the configuration is incident to a line of the configuration if and only if the duad corresponding to the point is one of the three pairs in the syntheme corresponding to the line.〔 The symmetric group of all permutations of the six elements underlying this system of duads and synthemes acts as a symmetry group of the Cremona–Richmond configuration, and gives the automorphism group of the configuration. Every flag of the configuration (an incident point-line pair) can be taken to every other flag by a symmetry in this group.〔; . The terminology of duads and synthemes is from , but Sylvester treats these systems of pairs and partitions in the context of a more general study of tuples and partitions of sets, does not reserve special attention to the case of a six-element set, and does not associate any geometric meaning to the sets.〕 The Cremona–Richmond configuration is self-dual: it is possible to exchange points for lines while preserving all the incidences of the configuration. This duality gives the Tutte–Coxeter graph additional symmetries beyond those of the Cremona–Richmond configuration, which swap the two sides of its bipartition. These symmetries correspond to the outer automorphisms of the symmetric group on six elements. 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「Cremona–Richmond configuration」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.