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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 Bracket polynomial ： ウィキペディア英語版 Bracket polynomial In the mathematical field of knot theory, the bracket polynomial (also known as the Kauffman bracket) is a polynomial invariant of framed links. Although it is not an invariant of knots or links (as it is not invariant under type I Reidemeister moves), a suitably "normalized" version yields the famous knot invariant called the Jones polynomial. The bracket polynomial plays an important role in unifying the Jones polynomial with other quantum invariants. In particular, Kauffman's interpretation of the Jones polynomial allows generalization to invariants of 3-manifolds. The bracket polynomial was discovered by Louis Kauffman in 1987. ==Definition== The bracket polynomial of any (unoriented) link diagram $L$, denoted $\backslash langle\; L\; \backslash rangle$, is a polynomial in the variable $A$, characterized by the three rules: * $\backslash langle\; O\; \backslash rangle\; =\; 1$, where $O$ is the standard diagram of the unknot * * $\backslash langle\; O\; \backslash cup\; L\; \backslash rangle\; =\; (-A^2\; -\; A^)\; \backslash langle\; L\; \backslash rangle$ The pictures in the second rule represent brackets of the link diagrams which differ inside a disc as shown but are identical outside. The third rule means that adding a circle disjoint from the rest of the diagram multiplies the bracket of the remaining diagram by $-A^2\; -\; A^$. 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「Bracket polynomial」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.