纽结理论是拓扑学的一个重要分支,虚拟纽结理论是经典纽结理论的推广,对它的研究是通过一种图解理论来展开的。虚拟纽结多项式是一类以多项式表达的虚拟纽结不变量,例如Arrow多项式和Wriggle多项式。Affine index多项式是以虚拟纽结图...纽结理论是拓扑学的一个重要分支,虚拟纽结理论是经典纽结理论的推广,对它的研究是通过一种图解理论来展开的。虚拟纽结多项式是一类以多项式表达的虚拟纽结不变量,例如Arrow多项式和Wriggle多项式。Affine index多项式是以虚拟纽结图的整数标记定义的单变量多项式。本文主要计算一类特殊虚拟纽结的Affine index多项式。按照Cheng着色的规则,对虚拟纽结图的每一段弧进行整数标记,计算每个经典交叉点的指标值,进而得到这类特殊虚拟纽结的Affine index多项式的表达式。Knot theory is an important branch of topology. Virtual knot theory is a generalization of classical knot theory, and its research is carried out through a graphic theory. The virtual knot polynomial refers to a class of virtual knot invariant expressed by polynomials, such as the Arrow polynomial and the Wriggle polynomial. The affine index polynomial is a univariate polynomial defined by the integer label of a virtual knot graph. In this paper, we mainly calculate affine index polynomials for a special class of virtual knots. According to the rules of Cheng coloring, we will integer label each arc of the virtual knot graph and calculate the index value of each classical crossings, and then get the expression of the affine index polynomial of this special virtual knot.展开更多
文摘纽结理论是拓扑学的一个重要分支,虚拟纽结理论是经典纽结理论的推广,对它的研究是通过一种图解理论来展开的。虚拟纽结多项式是一类以多项式表达的虚拟纽结不变量,例如Arrow多项式和Wriggle多项式。Affine index多项式是以虚拟纽结图的整数标记定义的单变量多项式。本文主要计算一类特殊虚拟纽结的Affine index多项式。按照Cheng着色的规则,对虚拟纽结图的每一段弧进行整数标记,计算每个经典交叉点的指标值,进而得到这类特殊虚拟纽结的Affine index多项式的表达式。Knot theory is an important branch of topology. Virtual knot theory is a generalization of classical knot theory, and its research is carried out through a graphic theory. The virtual knot polynomial refers to a class of virtual knot invariant expressed by polynomials, such as the Arrow polynomial and the Wriggle polynomial. The affine index polynomial is a univariate polynomial defined by the integer label of a virtual knot graph. In this paper, we mainly calculate affine index polynomials for a special class of virtual knots. According to the rules of Cheng coloring, we will integer label each arc of the virtual knot graph and calculate the index value of each classical crossings, and then get the expression of the affine index polynomial of this special virtual knot.
