Gauss codes for classical knots

Last updated 13th December, 2022.

Lists of Gauss codes derived from the Dowker-Thistlethwaite codes contained within knotscape are presented in the tables below. The lists use knotscape's ordering of codes and reference the corresponding Rolfsen number for knots up to ten crossings. The files for eight crossings and above contain both alternating and non-alternating codes.

The lists were created using the braid programme from input files containing the Dowker-Thistlethwaite codes extracted from knotscape's knot table. The knotscape codes do not contain any information about the sign of the crossings, since Dowker-Thistlethwaite codes are invariant under reflection in a line in the plane. The codes produced by the braid programme do include crossing signs, derived by an implementation of the same orientation algorithm used by knotscape.

A standard reference for classical knots up to ten crossings is the Rolfsen table at The Knot Atlas. The Gauss codes in the above lists are related to those given at The Knot Atlas site by a permutation of crossings. The following lists of planar diagram data for Gauss codes presented here may be helpful in reconciling them with those on The Knot Atlas. The data for eleven crossings and more is given for completeness.

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