纽结琼斯多项式与整系数多项式  

Knot Jones polynomials and integral coefficient polynomials

作　　者：韩友发[1] 马凯千 李欣璐 燕佳玉 HAN Youfa;MA Kaiqian;LI Xinlu;YAN Jiayu(School of Mathematics,Liaoning Normal University,Dalian 116081,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116081

出　　处：《辽宁师范大学学报（自然科学版）》2024年第3期289-293,共5页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(12026411)。

摘　　要：主要研究纽结琼斯多项式与整系数多项式之间的关系.利用纽结琼斯多项式的性质以及在某些点的特殊值,给出了宽度不同的整系数多项式为纽结琼斯多项式的成立条件.首先,给出了整系数多项式是某纽结Jones多项式的充分必要条件,给出了宽度为6的多项式是某一组结Jones多项式的充分必要条件.其次,主要研究Jones多项式与十一次整系数多项式的关系,研究宽度为9的十一次整系数多项式是琼斯多项式的必要条件,进而给出了某些纽结的Arf不变量.This paper primarily studies the relationship between the knot Jones polynomial and the integral coefficient polynomial.By examining the properties of the Jones polynomials and the special values at some points,we continue to study the integral coefficient polynomials with different degrees and widths as the establishment conditions of the Jones polynomials in knots.First,the sufficient and necessary conditions for an integral coefficient polynomial to be a Jones polynomial of a certain knot are presented.It shown that a polynomial of width six is a necessary and sufficient condition for Jones polynomial.Secondly,the relationship between Jones polynomial and polynomial with integral coefficients(11-degree).Specifically we explore the cases of 11-degree integer coefficient polynomial of width nine is Jones polynomial.Additionally,Arf invariants of some knots are given.

关 键 词：纽结琼斯多项式 宽度 整系数多项式 Arf不变量 

分 类 号：O189.3[理学—数学]