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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 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.
A conjecture of [swTAMS] states that a knot is nonfibered if and only if its infinite cyclic cover has uncountably many finite covers. We prove the conjecture for a class of knots that includes all knots of genus 1, using techniques from symbolic dynamics.
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