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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 L10a140 link ： ウィキペディア英語版 L10a140 link In the mathematical theory of knots, L10a140 is the name in the (Thistlewaite link table ) of a link of three loops, which has ten crossings between the loops when presented in its simplest visual form. It is of interest because it is presumably the simplest link which possesses the Brunnian property — a link of connected components that, when one component is removed, becomes entirely unconnected〔Adams, Colin C. (1994). ''The Knot Book'', . American Mathematical Society. ISBN 9780716723936.〕 — other than the six-crossing Borromean rings.〔Bar-Natan, Dror (2010-08-16). "(All Brunnians, Maybe )", ''Academic Pensieve''.〕 In other words, no two loops are directly linked with each other, but all three are collectively interlinked, so removing any loop frees the other two. In the image in the infobox at right, the red loop is not interlinked with either the blue or the yellow loops, and if the red loop is removed, then the blue and yellow loops can also be disentangled from each other without cutting either one. According to work by Slavik V. Jablan, the L10a140 link can be seen as the second in an infinite series of Brunnian links beginning with the Borromean rings. So if the blue and yellow loops have only one twist along each side, the resulting configuration is the Borromean rings; if the blue and yellow loops have three twists along each side, the resulting configuration is the L10a140 link; if the blue and yellow loops have five twists along each side, the resulting configuration is a three-loop link with 14 overall crossings, etc. etc.〔Jablan, Slavik V., ''Are Borromean Links So Rare?'', Forma 14 (1999), 269–277. Online at the electronic journal ''(Vismath )''. L10a140 is depicted in the middle figure of the top image.〕 ==Invariants== The (multivariable Alexander polynomial ) for the L10a140 link is : & = -\frac\left(t^5-2 t^4+t^3-2t^2+t-1\right) \left(t^5-t^4+2 t^3-t^2+2t-1\right) \\() & = w(t) w(1/t), \, \end where $w(t)\; =\; t^5-2\; t^4+t^3-2\; t^2+t-1.$ (Notice that $w(t)$ is essentially the Jones polynomial for the Whitehead link.) The HOMFLY polynomial is : $P(\backslash alpha,z)=z^\; \backslash alpha^-4z^2\; \backslash alpha^-4z^4\; \backslash alpha^-z^6\; \backslash alpha^-2z^+8z^2+12z^4+6z^6+z^8+z^\; \backslash alpha^2-4z^2\; \backslash alpha^2-4z^4\; \backslash alpha^2-z^6\; \backslash alpha^2,\; \backslash ,$ and the Kauffman polynomial is : $$ \begin F(a,z) & = 1 + 2z^ + a^z^ + a^z^ - 2a^z^ - az^ - 20z^2 + 2a^z^2 \\() & z^3 + 4a^ z^3 + 6a^ z^3 \\() & z^ \\() & - 9a^z^5 - 2a^ z^5 - 2az^5 - 9a^3 z^5 \\() & z^6 -11a^2 z^6 + 3a^4 z^6 + 4a^ z^7 \\() & z^8 + 4a^2 z^8 + 2a^ z^9 + 2az^9. \end 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「L10a140 link」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.