English

Coloring links by the symmetric group of degree three

Geometric Topology 2022-10-05 v2

Abstract

We consider the number of colors for the colorings of links by the symmetric group S3S_3 of degree 33. 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 S3S_3 with 4 or 5 colors. In this paper, we show that if a 2-bridge link admits a coloring by S3S_3 with 5 colors, then the link also admits such a coloring with only 4 colors.

Keywords

Cite

@article{arxiv.2112.02515,
  title  = {Coloring links by the symmetric group of degree three},
  author = {Kazuhiro Ichihara and Eri Matsudo},
  journal= {arXiv preprint arXiv:2112.02515},
  year   = {2022}
}

Comments

11 pages, 16 figures