This paper primarily studies the relationship between the knot Jones polynomial and the in-tegral 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 suffi-cient and necessary conditions for an integral coefficient polynomial to be a Jones polynomial of a cer-tain 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 inte-gral coefficients(11-degree).Specifically we explore the cases of 11-degree integer coefficient polyno-mial 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
Key words
knot Jones polynomial/width/polynomial with integral coefficient/Arf invariant
维普
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