ORIENTED STATE MODEL OF THE JONES POLYNOMIAL AND ITS CONNECTION TO THE DICHROMATIC POLYNOMIAL

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	ORIENTED STATE MODEL OF THE JONES POLYNOMIAL AND ITS CONNECTION TO THE DICHROMATIC POLYNOMIAL
	Jin,X ; Zhang,F ; Jin XA(金贤安)
刊名	http://dx.doi.org/10.1142/S0218216510007759
	2010-01
关键词	LINK POLYNOMIALS KNOTS INVARIANT GRAPHS
英文摘要	NSFC [10501038, 10671162, 10831001]; It is well known that Kauffman constructed a state model of the Jones polynomial based on unoriented link diagrams. In his approach, in order to obtain Jones polynomial one needs to calculate both the writhe and the Kauffman bracket. Stimulated by a paper of Altintas (An oriented state model for the Jones polynomial and its applications to alternating links, Appl. Math. Comput. 194 (2007) 168-178), in this paper we present a state sum model based on oriented link diagrams. In our approach, we succeed in adding the writhe to the state sum model and need not to compute the writher any more. We further show that, via our state sum model, Jones polynomial of any link (alternating or not) is a special parametrization of the dichromatic polynomial of a weighted graph with two different edge weights.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66805]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Jin,X,Zhang,F,Jin XA. ORIENTED STATE MODEL OF THE JONES POLYNOMIAL AND ITS CONNECTION TO THE DICHROMATIC POLYNOMIAL[J]. http://dx.doi.org/10.1142/S0218216510007759,2010.
APA	Jin,X,Zhang,F,&金贤安.(2010).ORIENTED STATE MODEL OF THE JONES POLYNOMIAL AND ITS CONNECTION TO THE DICHROMATIC POLYNOMIAL.http://dx.doi.org/10.1142/S0218216510007759.
MLA	Jin,X,et al."ORIENTED STATE MODEL OF THE JONES POLYNOMIAL AND ITS CONNECTION TO THE DICHROMATIC POLYNOMIAL".http://dx.doi.org/10.1142/S0218216510007759 (2010).