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  • In the mathematical field of knot theory, the Dowker notation, also called the Dowker–Thistlethwaite notation or code, for a knot is a sequence of even integers. The notation is named after Clifford Hugh Dowker and Morwen Thistlethwaite, who refined a notation originally due to Peter Guthrie Tait. To generate the Dowker notation, traverse the knot using an arbitrary starting point and direction. Label each of the n crossings with the numbers 1, ..., 2n in order of traversal, with the following modification: if the label is an even number and the strand followed crosses over at the crossing, then change the sign on the label to be a negative. When finished, each crossing will be labelled a pair of integers, one even and one odd. The Dowker notation is the sequence of even integer labels associated with the labels 1, 3, ..., 2n − 1 in turn. For example, a knot diagram may have crossings labelled with the pairs and. The Dowker notation for this labelling is the sequence: 6 −12 2 8 −4 −10. A knot can be recovered from a Dowker sequence, but the recovered knot may differ from the original by being a reflection or by having any connected sum component reflected in the line between its entry/exit points – the Dowker notation is unchanged by these reflections. Knots tabulations typically consider only prime knots and disregard chirality, so this ambiguity does not affect the tabulation. Wikipedia