| Knots and Polynomials |
| Received:June 01, 2008 Revised:October 06, 2008 |
| Key Words:
knot Jones polynomial Laurent polynomial.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10771023) and the Liaoning Educational Committee (Grant No.2009A418). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.02.008 |
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