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arXiv · 2105.10921

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

Michał Jabłonowski
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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.

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Michał Jabłonowski. 2021-05-23. Tabulation of knots up to five triple-crossings and moves between oriented diagrams. https://doi.org/10.3836/tjm%2F1502179382

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