纽结多项式与整系数多项式的性质  

Properties of Knot Jones Polynomials and Integral Coefficient Polynomials

作　　者：谭雅文 李欣璐 韩友发[1] 

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》2024年第7期3078-3085,共8页Advances in Applied Mathematics

摘　　要：文章主要研究纽结琼斯多项式与整系数多项式之间的关系。主要研究某些次数不同、宽度不同的整系数多项式与Jones多项式的关系。研究侧重点是在何种条件下,一定宽度的九次、十三次次整系数多项式是某纽结琼斯多项式,给出了满足条件的例子,再令某些系数为特殊值,给出次数相同宽度不同的多项式是某纽结琼斯多项式的判别方法。进而给出了某些纽结的Arf不变量。This paper mainly studies the relationship between the knot Jones polynomial and the integral coefficient polynomial. We mainly study the relationship between some integer coefficients polynomials with different degrees and widths and Jones polynomials. The research focuses on the following conditions: Under which conditions, the ninth-degree, thirteenth-degree, integral coefficient polynomial of a certain width is the Jones polynomial of a knot. The examples satisfying the conditions are given, and then some coefficients are set as special values, and it is deduced that polynomials with the same degree and different widths are the discriminant methods for certain knotJones polynomials, and their coefficients satisfy specific quantitative laws, and then give Arf invariants of some knots.

关 键 词：纽结多项式 宽度 整系数多项式 Arf不变量 

分 类 号：O17[理学—数学]