Braid Notation

Here we give a braid representation of each knot. These were taken from [1], which gives the minimum length braid in each case. In all cases except the knot 10136, this also gives the number of strands. For that knot, we also give a braid with the minimum number of strands, taken from [2], as referred to by Gittings. For 11 crossing knots, when the braid length does not come from a minimal stranded braid, a minimal stranded braid is given, as provided by Alexander Stoimenow.

References

[1] Gittings, T., "Minimum Braids: A Complete Invariant of Knots and Links," Arxiv preprint.

[2] Jones, V. F. R., "Hecke algebra representations for braid groups and link polynomials," Ann. of Math., 126 (1987), 335-388.

[3] Stoimenow, A., Personal communication.