纽结与多项式

In this paper, we deal with some corresponding relations between knots and polynomials by using the basic properties of knot polynomials （such as, some special values of knot polynomials, the Arf invariant and derivative of knot polynomials）. We give necessary and sufficient conditions that a Laurent polynomial with integer coefficients, whose breadth is less than five, is the Jones polynomial of a certain knot.     

纽结多项式和整系数多项式

基于纽结多项式性质研究了整系数多项式及其性质,讨论了常系数项为0的6次和7次整系数多项式和纽结多项式的关系,给出了整系数多项式是纽结多项式的充分必要条件,进而给出了整系数多项式是交错纽结的多项式的充分必要条件.根据这些性质进一步给出了某些纽结的Arf不变量的性质.