整系数多项式与纽结多项式

Knot Polynomials and Integral Coefficient Polynomials

摘要: 本文主要研究了整系数多项式和纽结Jones多项式的相关性质和二者之间的关系。研究宽度为7的多项式是某纽结Jones多项式的条件。先后介绍了宽度为5的多项式和宽度为6的多项式是某纽结Jones多项式的充分必要条件，在此基础上引出了宽度为7的多项式是某纽结Jones多项式的必要条件的研究。讨论了十二次整系数多项式与Jones多项式的一些关系。若一个Laurent多项式是一个次数为12，宽度为8的整系数多项式，给出了它是Jones多项式的必要条件。

Abstract: In this paper, we studied the properties of integral coefficient polynomial and knot polynomial, and the relationship between them. The paper mainly studied conditions that the polynomial with breadth 7 is the Jones polynomial of a knot; introduced sufficient and necessary condition that an integral coefficient polynomial with breadth 5 or 6 is the Jones polynomial of a knot. Next, we stud-ied necessary condition that polynomial with width 7 is the Jones polynomial of a knot; discussed some relations between integral coefficients polynomials of degree 12 and the Jones polynomial. If a polynomial is an integral coefficient polynomial of degree 12 and width 8, we can find the necessary conditions for it to be a polynomial.