Knot Polynomials And Integral Coefficient Polynomials

In this paper,the knowledge of integral coefficient polynomial and knot polynomial is studied and the their relationship is focus.In the first part,this chapter introduces the preparatory knowledge related to the paper.Secondly,the properties of Alexander polynomials are introduced.Finally,the properties of polynomials are introduced.In the second part,this chapter mainly studies the width of 7 polynomial is a sufficient and necessary conditions of knot polynomial.First introduced the width of 5 polynomial is sufficient and necessary condition of a knot polynomial,the width is introduced for 6 polynomial is sufficient and necessary condition of a knot polynomial,finally studies the polynomial width is 7 is a sufficient and necessary conditions of knot polynomial.In the third part,this chapter mainly discusses some relations between polynomials of twelve integral coefficients.First,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.If a polynomial is an integral coefficient polynomial of degree 12 and width 9,then we can find the necessary condition for it to be polynomial.In the fourth part,this chapter mainly discusses some relations between integral coefficient polynomials and polynomials.If a polynomial is an integral coefficient polynomial of degree 12 and the constant term is not 0,then we can find the necessary conditions for it to be polynomial.If a polynomial is an integral coefficient polynomial of degree 13 and the constant term is not 0,then we can find that it is a necessary condition for polynomial.