论文标题
结多项式的单样减少
Monomial reduction of knot polynomials
论文作者
论文摘要
对于所有自然数量$ n $和Prime $ P $，我们找到一个结$ K $，其skein polyenmial $ p_k（a，z）$在$ z = n $上评估的$ z = n $具有微不足道的减少Modulo $ p $。我们建筑的一个有趣的结果是，所有多项式$ p_k（a，n）$（mod〜 $ p $）都用有界的编织索引来实现有界$ a $ span的界面。作为一个应用程序，我们将表单$ p_k（a，1）$（mod $ 2 $）的所有多项式分类为$ a $ span $ \ leq 10 $。
For all natural numbers $N$ and prime numbers $p$, we find a knot $K$ whose skein polynomial $P_K(a,z)$ evaluated at $z=N$ has trivial reduction modulo $p$. An interesting consequence of our construction is that all polynomials $P_K(a,N)$ (mod~$p$) with bounded $a$-span are realised by knots with bounded braid index. As an application, we classify all polynomials of the form $P_K(a,1)$ (mod $2$) with $a$-span $\leq 10$.
