English

Tabulation of knots up to five triple-crossings and moves between oriented diagrams

Geometric Topology 2023-07-06 v2 Combinatorics

Abstract

We enumerate and show tables of minimal diagrams for all prime knots up to the triple-crossing number equal to five. We derive a minimal generating set of oriented moves connecting triple-crossing diagrams of the same oriented knot. We also present a conjecture about a strict lower bound of the triple-crossing number of a knot related to the breadth of its Alexander polynomial.

Keywords

Cite

@article{arxiv.2105.10921,
  title  = {Tabulation of knots up to five triple-crossings and moves between oriented diagrams},
  author = {Michał Jabłonowski},
  journal= {arXiv preprint arXiv:2105.10921},
  year   = {2023}
}

Comments

15 pages, many TikZ figures