Coloring links by the symmetric group of degree three

Kazuhiro Ichihara; Eri Matsudo

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arXiv · 2112.02515

Coloring links by the symmetric group of degree three

Kazuhiro Ichihara·Eri Matsudo

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Abstract

We consider the number of colors for the colorings of links by the symmetric group $S_3$ 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 $S_3$ with 4 or 5 colors. In this paper, we show that if a 2-bridge link admits a coloring by $S_3$ with 5 colors, then the link also admits such a coloring with only 4 colors.

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Kazuhiro Ichihara, Eri Matsudo. 2021-12-05. Coloring links by the symmetric group of degree three. https://arxiv.org/abs/2112.02515

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