On the location of zeros of the Homfly polynomial

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	On the location of zeros of the Homfly polynomial
	Jin, Xian'an ; Zhang, Fuji ; Zhang FJ(张福基) ; Jin XA(金贤安)
刊名	http://dx.doi.org/10.1088/1742-5468/2011/07/P07011
	2011-07
关键词	JONES POLYNOMIALS LINK POLYNOMIALS STATISTICAL-MECHANICS TUTTE POLYNOMIALS CHROMATIC ROOTS PRETZEL LINKS COMPLEX-PLANE KNOT-THEORY GRAPHS INVARIANTS
英文摘要	National Natural Science Foundation of China [10831001]; Fundamental Research Funds for the Central Universities [2010121007]; Wu, Wang, Chang and Shrock initiated the study of zeros of the Jones polynomial since it was the special case of partition functions of the Potts model in physics. The Homfly polynomial is the generalization of the Jones polynomial. Let L be an oriented link, and P(L)(v, z) be its Homfly polynomial. In this paper, we study zeros of P(L)(v, z) with z fixed. We prove the so-called unit-circle theorem for a family of generalized Jaeger's links {Dn(G)\| n = 1, 2, ...} which states that \|v\| = 1 is the limit of zeros of Homfly polynomials of generalized Jaeger's links {Dn(G)\| n = 1, 2, ...} if G is bridgeless. Similar to the result of the Jones polynomial, we also prove that zeros of Homfly polynomials are dense in the whole complex plane.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66343]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Jin, Xian'an,Zhang, Fuji,Zhang FJ,et al. On the location of zeros of the Homfly polynomial[J]. http://dx.doi.org/10.1088/1742-5468/2011/07/P07011,2011.
APA	Jin, Xian'an,Zhang, Fuji,张福基,&金贤安.(2011).On the location of zeros of the Homfly polynomial.http://dx.doi.org/10.1088/1742-5468/2011/07/P07011.
MLA	Jin, Xian'an,et al."On the location of zeros of the Homfly polynomial".http://dx.doi.org/10.1088/1742-5468/2011/07/P07011 (2011).