Open Access
May 2014 Polynomials, Binary Trees, and Positive Braids
Chad Wiley, Jeffrey Gray
Missouri J. Math. Sci. 26(1): 1-13 (May 2014). DOI: 10.35834/mjms/1404997104


In knot theory, a common task is to take a given knot diagram and generate from it a polynomial. One method for accomplishing this is to employ a skein relation to convert the knot into a type of labeled binary tree and from this tree derive a two-variable polynomial. The purpose of this paper is to determine, in a simplified setting, which polynomials can be generated from labeled binary trees. We give necessary and sufficient conditions for a polynomial to be constructible in this fashion and we will provide a method for reconstructing the generating tree from such a polynomial. We conclude with an application of this theorem to a class of knots and links given by closed positive braids.


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Chad Wiley. Jeffrey Gray. "Polynomials, Binary Trees, and Positive Braids." Missouri J. Math. Sci. 26 (1) 1 - 13, May 2014.


Published: May 2014
First available in Project Euclid: 10 July 2014

zbMATH: 1297.57025
MathSciNet: MR3229945
Digital Object Identifier: 10.35834/mjms/1404997104

Primary: 05C05
Secondary: 05C31

Keywords: binary trees , Knot polynomials , Positive braids , Skein relations

Rights: Copyright © 2014 Central Missouri State University, Department of Mathematics and Computer Science

Vol.26 • No. 1 • May 2014
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