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.
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