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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 Toida's conjecture ： ウィキペディア英語版 Toida's conjecture In combinatorial mathematics, Toida's conjecture, due to Shunichi Toida in 1977,〔 *S. Toida: "A note on Adam's conjecture", J. of Combinatorial Theory (B), pp. 239–246, October–December 1977〕 is a refinement of the disproven Ádám's conjecture in 1967. Toida's conjecture states formally: If :''S'' is a subset of $\backslash mathbb^$ *_n and :$\backslash vec\; =\; \backslash vec(\; \backslash mathbb\_n\; ;\; S\; )$ then ''$\backslash vec$'' is a CI-digraph. ==Proofs== The conjecture was proven in the special case where ''n'' is a prime power by Klin and Poschel in 1978,〔 *Klin, M.H. and R. Poschel: The Konig problem, the isomorphism problem for cyclic graphs and the method of Schur rings, Algebraic methods in graph theory, Vol. I, II., Szeged, 1978, pp. 405–434.〕 and by Golfand, Najmark, and Poschel in 1984.〔 *Golfand, J.J., N.L. Najmark and R. Poschel: The structure of S-rings over Z2m , preprint (1984).〕 The conjecture was then fully proven by Muzychuk, Klin, and Poschel in 2001 by using Schur algebra,〔Klin, M.H., M. Muzychuk and R. Poschel: The isomorphism problem for circulant graphs via Schur ring theory, Codes and Association Schemes, American Math. Society, 2001.〕 and simultaneously by Dobson and Morris in 2002 by using the classification of finite simple groups.〔 *E. Dobson, J. Morris: TOIDA’S CONJECTURE IS TRUE, PhD Thesis, 2002.〕 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「Toida's conjecture」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.