虚拟纽结的一新多项式  

A New Polynomial of Virtual Knots

作　　者：张宇涵 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《应用数学进展》2025年第2期40-49,共10页Advances in Applied Mathematics

摘　　要：虚拟纽结理论中主要研究对象为纽结和链环。虚拟纽结多项式是一类以多项式表达的虚拟纽结不变量,例如零多项式和Writhe多项式。文章通过研究零多项式和虚拟链环的writhe多项式给出了一个新的多项式。这个多项式通过对虚拟链环的计算得出原始虚拟纽结的多项式,证明了这个多项式是一虚拟纽结不变量,给出了其性质及一实例计算。The main research objects of virtual knot theory are knot and link. Virtual knot polynomials are a class of virtual knot invariants expressed as polynomials, such as the zero polynomial and the writhe polynomial. In this paper, a new polynomial is given by studying zero polynomials and writhe polynomials of virtual links. The polynomial of the original virtual knot is obtained by computing the virtual link. It proves that the polynomial is a virtual knot invariant, and properties and computational examples are given.

关 键 词：虚拟纽结不变量 Writhe多项式 高斯图 

分 类 号：O17[理学—数学]