Editing Knot theory (section)

===Dowker–Thistlethwaite notation===
{{main|Dowker–Thistlethwaite notation}}
[[File:Dowker-notation-example.svg|thumb|upright=.85|A knot diagram with crossings labelled for a Dowker sequence]]
The [[Dowker–Thistlethwaite notation]], also called the Dowker notation or code, for a knot is a finite sequence of even integers. The numbers are generated by following the knot and marking the crossings with consecutive integers. Since each crossing is visited twice, this creates a pairing of even integers with odd integers. An appropriate sign is given to indicate over and undercrossing. For example, in this figure the knot diagram has crossings labelled with the pairs (1,6) (3,&minus;12) (5,2) (7,8) (9,&minus;4) and (11,&minus;10). The Dowker–Thistlethwaite notation for this labelling is the sequence: 6, &minus;12, 2, 8, &minus;4, &minus;10. A knot diagram has more than one possible Dowker notation, and there is a well-understood ambiguity when reconstructing a knot from a Dowker–Thistlethwaite notation.