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**Polynomials, binary trees, and positive braids.**
*(English)*
Zbl 1297.57025

Summary: 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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\textit{C. Wiley} and \textit{J. Gray}, Missouri J. Math. Sci. 26, No. 1, 1--13 (2014; Zbl 1297.57025)

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### References:

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