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The colored Kauffman Skein relation and the head and tail of the colored Jones polynomial

Mustafa Hajij

Mustafa Hajij

Department of Mathematics, University of South Florida, Tampa, FL 33647, USA

E-mail Address: mhajij@math.usf.edu

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https://doi.org/10.1142/S0218216517410024Cited by:4 (Source: Crossref)

Abstract

Using the colored Kauffman skein relation, we study the highest and lowest $4 n$ coefficients of the $n th$ unreduced colored Jones polynomial of alternating links. This gives a natural extension of a result by Kauffman in regard with the Jones polynomial of alternating links and its highest and lowest coefficients. We also use our techniques to give a new and natural proof for the existence of the tail of the colored Jones polynomial for alternating links.

Keywords:

AMSC: 57M25, 57M27

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