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Kauffman polynomial

Kauffman 多项式

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Mathematical Physics: Classical Mechanics 封面

《Mathematical Physics: Classical Mechanics》 · 第 173–174 页 · Chapter 15,Definition 15.3 与完整 Theorem 15.5;原页图式保留条件 (iii)、(iv) 与 Figure 15.6

The Kauffman polynomial is the function \(F:\{\text{Oriented links in }S^3\}\longrightarrow\mathbb Z[a^{\pm1},z^{\pm1}]\) defined by \(F(L)=a^{-w(D)}\Lambda(D)\), where \(D\) is a diagram with writhe \(w(D)\) of the oriented link \(L\) and \(\Lambda\) is the function of the next theorem. […] There exists a function \(\Lambda:\{\text{Unoriented links diagrams in }S^2\}\longrightarrow\mathbb Z[a^{\pm1},z^{\pm1}]\) that is defined uniquely by the following: (i) \(\Lambda(U)=1\), where \(U\) is the zero-crossing diagram of the unknot;

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