Dowker–Thistlethwaite notation

The notation is named after Clifford Hugh Dowker and Morwen Thistlethwaite, who refined a notation originally due to Peter Guthrie Tait.

[1] To generate the Dowker–Thistlethwaite notation, traverse the knot using an arbitrary starting point and direction.

When finished, each crossing will be labelled a pair of integers, one even and one odd.

Dowker and Thistlethwaite have proved that the notation specifies prime knots uniquely, up to reflection.

[1] In the more general case, a knot can be recovered from a Dowker–Thistlethwaite sequence, but the recovered knot may differ from the original by either being a reflection or by having any connected sum component reflected in the line between its entry/exit points – the Dowker–Thistlethwaite notation is unchanged by these reflections.