Tables of Positive Braid Knots

This dataset extends the known tables of positive braid knots (e.g., by Lukas Lewark, Alex Stoimenow, and KnotInfo) to higher crossing numbers.

Dataset Summary:

17 Crossings: 369 knots
18 Crossings: 353 knots
19 Crossings: 2033 knots

The complete list includes names based on Benjamin Burton's catalog.

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Preview (Top 6 Entries)

Knot Name (Burton)	Braid Word
17at_1	`11111111111111111`
17ns_12	`11111211123321123`
17nh_0000008	`11112111223221123`
17nh_0000010	`11111211123221123`
17nh_0000014	`11121132213221322`
17nh_0000023	`11111112113221332`

Credits & References:

Knot names for crossing numbers 17, 18, and 19 are based on:
Benjamin A. Burton, The next 350 million knots, 36th International Symposium on Computational Geometry (SoCG 2020), Leibniz Int. Proc. Inform., vol. 164, 2020.

Data compiled by Michael Gasser.