Coloring links by the symmetric group of degree three
Abstract
We consider the number of colors for the colorings of links by the symmetric group S3 of degree 3. For knots, such a coloring corresponds to a Fox 3-coloring, and thus the number of colors must be 1 or 3. However, for links, there are colorings by S3 with 4 or 5 colors. In this paper, we show that if a 2-bridge link admits a coloring by S3 with 5 colors, then the link also admits such a coloring with only 4 colors.
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