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 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.
@article{bwmeta1.element.bwnjournal-article-bcpv42i1p381bwm,
author = {Silver, Daniel and Williams, Susan},
title = {Generalized n-colorings of links},
journal = {Banach Center Publications},
volume = {43},
year = {1998},
pages = {381-394},
zbl = {0903.57004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p381bwm}
}
Silver, Daniel; Williams, Susan. Generalized n-colorings of links. Banach Center Publications, Tome 43 (1998) pp. 381-394. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p381bwm/
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