基于分裂状态的规范伪括号多项式计算方法  

A calculation method for normalized pseudo bracket polynomials based on splitting states

作　　者：鄂强 张志艳 E Qiang;ZHANG Zhi-yan(School of Science,Dalian Maritime University,Dalian 116033,China)

机构地区：[1]大连海事大学理学院,辽宁大连116033

出　　处：《吉林师范大学学报（自然科学版）》2022年第4期57-62,共6页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(11671064);中央高校基本科研项目(3132022205)。

摘　　要：介绍了伪纽结理论的相关概念和主要结论,将计算纽结Kauffman多项式的方法推广到伪纽结的规范伪括号多项式,提出了一种基于伪纽结的全部分裂状态的规范伪括号多项式的计算方法.根据这一方法,计算了含有不同数目的伪交叉点的伪三叶结投影图的规范伪括号多项式,结果表明,它们是不等价的伪纽结,赋权解集不是伪纽结的完全不变量.It was introduced related definitions and main results of the pseudo knot theory.The method of calculating Kauffman polynomials was extended to the normalized pseudo bracket polynomials of pseudo knots.A method for calculating the normalized pseudo bracket polynomial was proposed by considering all the splitting states of a pseudo knot.According to this method,the normalized pseudo bracket polynomials of pseudo trefoils with different numbers of precrossings was calculated.The results showed that they are not equivalent,and the weighted resolution set is not a complete invariant of pseudo knots.

关 键 词：纽结理论 伪纽结 纽结不变量 伪括号多项式 

分 类 号：O189.24[理学—数学]