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

    Stoimenow, A. 2015. Application of braiding sequences III: Concordance of positive knots. International Journal of Mathematics, Vol. 26, Issue. 07, p. 1550050.


    PRZYTYCKI, JÓZEF H. and TANIYAMA, KOUKI 2010. ALMOST POSITIVE LINKS HAVE NEGATIVE SIGNATURE. Journal of Knot Theory and Its Ramifications, Vol. 19, Issue. 02, p. 187.


    STOIMENOW, A. 2010. APPLICATION OF BRAIDING SEQUENCES, I: ON THE CHARACTERIZATION OF VASSILIEV AND POLYNOMIAL LINK INVARIANTS. Communications in Contemporary Mathematics, Vol. 12, Issue. 05, p. 681.


    Stoimenow, A. 2007. Square numbers and polynomial invariants of achiral knots. Mathematische Zeitschrift, Vol. 255, Issue. 4, p. 703.


    Silver, Daniel S Stoimenow, Alexander and Williams, Susan G 2006. Euclidean Mahler measure and twisted links. Algebraic & Geometric Topology, Vol. 6, Issue. 2, p. 581.


    Hoste, Jim Thistlethwaite, Morwen and Weeks, Jeff 1998. The first 1,701,936 knots. The Mathematical Intelligencer, Vol. 20, Issue. 4, p. 33.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 106, Issue 2
  • September 1989, pp. 273-276

The skein polynomial of a planar star product of two links

  • Kunio Murasugi (a1) and Jozef H. Przytycki (a2)
  • DOI: http://dx.doi.org/10.1017/S0305004100078099
  • Published online: 28 June 2011
Abstract
Abstract

If PL(v,z) = Σbi(v)zi is the skein polynomial of a link L, and D = D1 * D2 is the diagram which is a planar star (Murasugi) product of D1 and D2 then bϕ(D)(v) = bϕ(D1)·bϕ(D2)(v) where ϕ(D) = n(D)– (s(D) – 1) and n(D) denotes the number of crossings of D, and s(D) is the number of Seifert circles of D.

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[3] P. Freyd , D. Yetter , J. Hoste , W. B. R. Lickorish , K. Millett and A. Ocneanu . A new polynomial invariant of knots and links. Bull. Amer. Math. Soc. 12 (1985), 239249.

[8] K. Murasugi . On a certain numerical invariant of link types. Trans. Amer. Math. Soc. 117 (1965), 387422.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
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