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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 Upper bound theorem ： ウィキペディア英語版 Upper bound theorem In mathematics, the upper bound theorem states that cyclic polytopes have the largest possible number of faces among all convex polytopes with a given dimension and number of vertices. It is one of the central results of polyhedral combinatorics. Originally known as the upper bound conjecture, this statement was formulated by Theodore Motzkin, proved in 1970 by Peter McMullen, and strengthened from polytopes to subdivisions of a sphere in 1975 by Richard P. Stanley. ==Cyclic polytopes== (詳細はconvex hull of ''n'' vertices on the moment curve (''t'', ''t''2, ''t''3, ...). The precise choice of which ''n'' points on this curve are selected is irrelevant for the combinatorial structure of this polytope. The number of ''i''-dimensional faces of ''Δ''(''n'',''d'') is given by the formula : $f\_i(\backslash Delta(n,d))\; =\; \backslash binom\; \backslash quad\; \backslash textrm\; \backslash quad$ 0 \leq i < \left() and $(f\_0,\backslash ldots,f\_"\; TITLE="\backslash frac">)-1\})$ completely determine $(f\_"\; TITLE="\backslash frac">)\},\backslash ldots,f\_)$ via the Dehn–Sommerville equations. The same formula for the number of faces holds more generally for any neighborly polytope. 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「Upper bound 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.