arXiv Analytics

Sign in

arXiv:2105.10921 [math.GT]AbstractReferencesReviewsResources

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

Michał Jabłonowski

Published 2021-05-23Version 1

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.

Comments: 15 pages, many TikZ figures
Categories: math.GT, math.CO
Related articles: Most relevant | Search more
arXiv:2208.08244 [math.GT] (Published 2022-08-17)
Minimal generating sets of moves for surfaces immersed in the four-space
arXiv:0908.3127 [math.GT] (Published 2009-08-21, updated 2010-07-22)
Minimal generating sets of Reidemeister moves
arXiv:1306.5382 [math.GT] (Published 2013-06-23)
A minimal generating set of the level 2 mapping class group of a non-orientable surface

Links

Toolbox