CAJ | 학술논문

本文利用纽结Jones多项式的性质研究了整系数多项式的性质，主要研究了某些宽度是5的7次和8次整系数多项式和纽结多项式的关系，给出整系数多项式是纽结多项式的充分必要条件，进而给出整系数多项式是交错纽结的Jones多项式的充分必要条件。同时根据这些性质给出了某些交错纽结的Arf不变量。
본문이용뉴결Jones다항식적성질연구료정계수다항식적성질，주요연구료모사관도시5적7차화8차정계수다항식화뉴결다항식적관계，급출정계수다항식시뉴결다항식적충분필요조건，진이급출정계수다항식시교착뉴결적Jones다항식적충분필요조건。동시근거저사성질급출료모사교착뉴결적Arf불변량。
In this paper,we studied the properties of polynomials with integer coefficients by using the properties of the Jones polynomial. We discussed mainly the relations between polynomials of knots and polynomials with in-teger coefficients,which the breath of these polynomials is 5 and the degree of the polynomials is 7 or 8. We gave sufficient and necessary conditions that the polynomials are the Jones polynomials of some knots and gave neces-sary and sufficient conditions that the polynomials are the Jones polynomials of some alternating knots. We ob-tained the properties of the Arf invariant of some knots.