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The skein polynomial of a planar star product of two links

Published online by Cambridge University Press:  28 June 2011

Kunio Murasugi  and
Jozef H. Przytycki
Kunio Murasugi
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1
Jozef H. Przytycki
Affiliation:
Department of Mathematics, Warsaw University, Warsaw, Poland 00901
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 2 , September 1989 , pp. 273 - 276
Copyright
Copyright © Cambridge Philosophical Society 1989

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