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A note on the Lickorish-Millett-Turaev formula for the Kauffman polynomial

We use the idea of expressing a nonoriented link as a sum of all oriented links corresponding to the link to present a short proof of the Lickorish-Millett-Turaev formula for the Kauffman polynomial at $z= -a- a^{-1}$. Our approach explains the observation made by Lickorish and Millett that the formula is the generating function for the linking number of a sublink of the given link with its complementary sublink.

preprint2012arXivOpen access
Jozef H. Przytycki
math.GT
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Jozef H. Przytycki

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