亞歷山大多項式

在纽结理论中，亚历山大多项式（Alexander polynomial）是一种紐結多項式。

亚历山大–康威多项式

• $\mathrm{\nabla }(O)=1$ (unknot)
• $\mathrm{\nabla }(L_{+})-\mathrm{\nabla }(L_{-})=z\mathrm{\nabla }(L_0)$

${\mathrm{\Delta }}_L(t^2)={\mathrm{\nabla }}_L(t-t^{-1})$

$\mathrm{\Delta }(L_{+})-\mathrm{\Delta }(L_{-})=(t^{1/2}-t^{-1/2})\mathrm{\Delta }(L_0)$

阅读

• Template:Cite journal
• Template:Cite book
• Template:Cite book (accessible introduction utilizing a skein relation approach)
• Template:Cite journal
• Template:Cite book
• Template:Cite journal
• Template:Cite book
• Template:Cite book (covers several different approaches, explains relations between different versions of the Alexander polynomial)
• Template:Cite journal
• Template:Cite journal
• Template:Cite journal
• Template:Cite thesis
• Template:Cite book (explains classical approach using the Alexander invariant; knot and link table with Alexander polynomials)

外部链接

• Template:Springer
• "Main Page" and "The Alexander-Conway Polynomial", The Knot Atlas. – knot and link tables with computed Alexander and Conway polynomials