翻訳と辞書 Words near each other ・ Radnorshire Arms ・ Radnorshire Society Transactions ・ Radnorshire Wildlife Trust ・ Radnovac ・ Radnovce ・ Rado ・ Rado (mayor of the palace) ・ Rado (palatine) ・ Rado (watchmaker) ・ Rado graph ・ Rado Krošelj ・ Rado Lenček ・ Rado Riha ・ Rado Vidošić ・ Rado's theorem ・ Rado's theorem (Ramsey theory) ・ Radoald of Benevento ・ Radobica ・ Radobić ・ Radoblje ・ Radoboj ・ Radobolja ・ Radobuđa ・ Radobýl ・ Radoceras ・ Radochów ・ Radocin ・ Radocyna ・ Radocza ・ Radoevtsi 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 Rado's theorem (Ramsey theory) ： ウィキペディア英語版 Rado's theorem (Ramsey theory) Rado's theorem is a theorem from the branch of mathematics known as Ramsey theory. It is named for the German mathematician Richard Rado. It was proved in his thesis, ''Studien zur Kombinatorik''. Let $A\; \backslash mathbf\; =\; \backslash mathbf$ be a system of linear equations, where $A$ is a matrix with integer entries. This system is said to be $r$''-regular'' if, for every $r$-coloring of the natural numbers 1, 2, 3, ..., the system has a monochromatic solution. A system is ''regular'' if it is ''r-regular'' for all ''r'' ≥ 1. Rado's theorem states that a system $A\; \backslash mathbf\; =\; \backslash mathbf$ is regular if and only if the matrix ''A'' satisfies the ''columns condition''. Let ''ci'' denote the ''i''-th column of ''A''. The matrix ''A'' satisfies the columns condition provided that there exists a partition ''C''1, ''C''2, ..., ''C''''n'' of the column indices such that if $s\_i\; =\; \backslash Sigma\_c\_j$, then # ''s''1 = 0 # for all ''i'' ≥ 2, ''si'' can be written as a rational〔Modern graph theory by Béla Bollobás. 1st ed. 1998. ISBN 978-0-387-98488-9. Page 204〕 linear combination of the ''cjs in the ''Ck'' with ''k'' < ''i''. Folkman's theorem, the statement that there exist arbitrarily large sets of integers all of whose nonempty sums are monochromatic, may be seen as a special case of Rado's theorem concerning the regularity of the system of equations :$x\_T\; =\; \backslash sum\_x\_\{\backslash \{i\backslash \}\},$ where ''T'' ranges over each nonempty subset of the set 〔.〕 ==References== 〔 Category:Theorems in discrete mathematics 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「Rado's theorem (Ramsey theory)」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.