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  • Cited by 4
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    BLAIR, RYAN C. 2009. ALTERNATING AUGMENTATIONS OF LINKS. Journal of Knot Theory and Its Ramifications, Vol. 18, Issue. 01, p. 67.


    NICHOLSON, NEIL R. 2008. NONALTERNATING KNOTS AND JONES POLYNOMIALS. Journal of Knot Theory and Its Ramifications, Vol. 17, Issue. 08, p. 983.


    BAE, YONGJU and MORTON, HUGH R. 2003. THE SPREAD AND EXTREME TERMS OF JONES POLYNOMIALS. Journal of Knot Theory and Its Ramifications, Vol. 12, Issue. 03, p. 359.


    Cromwell, P. R. 1991. Lonely knots and tangles: Identifying knots with no companions. Mathematika, Vol. 38, Issue. 02, p. 334.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 103, Issue 3
  • May 1988, pp. 451-456

An upper bound for the breadth of the Jones polynomial

  • Morwen B. Thistlethwaite (a1)
  • DOI: http://dx.doi.org/10.1017/S030500410006504X
  • Published online: 24 October 2008
Abstract

In the recent article [2], a kind of connected link diagram called adequate was investigated, and it was shown that the Jones polynomial is never trivial for such a diagram. Here, on the other hand, upper bounds are considered for the breadth of the Jones polynomial of an arbitrary connected diagram, thus extending some of the results of [1,4,5]. Also, in Theorem 2 below, a characterization is given of those connected, prime diagrams for which the breadth of the Jones polynomial is one less than the number of crossings; recall from [1,4,5] that the breadth equals the number of crossings if and only if that diagram is reduced alternating. The article is concluded with a simple proof, using the Jones polynomial, of W. Menasco's theorem [3] that a connected, alternating diagram cannot represent a split link. We shall work with the Kauffman bracket polynomial 〈D〉 ∈ Z[A, A−1 of a link diagram D.

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[3]W. Menasco . Closed incompressible surfaces in alternating knot and link complements. Topology 23 (1984), 3744.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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