一类链环的Writhe多项式及性质
The Writhe Polynomials and Properties of a Class of Links

Writhe多项式在虚拟纽结理论中占据一定地位。Writhe多项式与虚拟纽结的虚拟交叉点数下界存在一定联系，并可以找到与利用奇writhe多项式和Henrich的多项式中任何一个判断出来的forbidden数下界相比一样强或更强的下界。本文针对给出的一类虚拟纽结，计算出其writhe多项式并利用writhe多项式和二阶writhe多项式研究其虚拟交叉点数的下界和forbidden数的下界，同时还讨论了writhe多项式和二阶writhe多项式对该类虚拟纽结和其突变体的影响。
The writhe polynomial occupies a certain position in virtual knot theory. The writhe polynomial has some relationship with the virtual crossing number lower bound of the virtual knot, and can find a lower bound as strong or stronger than the forbidden number lower bound judged using either of the odd writhe polynomial and Henrich’s polynomial. In this paper, writhe polynomials are calculated for a class of virtual knots, the writhe polynomial and the second-order writhe polynomial are used to study a lower bound of virtual crossing number and a lower bound of the forbidden number for a class of virtual knots, and the effects of the writhe polynomial and the second-order writhe polynomial on the virtual knots and their mutants are also discussed.