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1998 | 42 | 1 | 381-394
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Generalized n-colorings of links

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The notion of an (n,r)-coloring for a link diagram generalizes the idea of an n-coloring introduced by R. H. Fox. For any positive integer n the various (n,r)-colorings of a diagram for an oriented link l correspond in a natural way to the periodic points of the representation shift $Φ_{𝒁/n}(l)$ of the link. The number of (n,r)-colorings of a diagram for a satellite knot is determined by the colorings of its pattern and companion knots together with the winding number.
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  • Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688, U.S.A.
  • Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688, U.S.A.
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