Unique Conway notation for knots?

The first answer is correct -- because notation is for diagrams, of which there are many for any single knot. Conway's continued fraction solves this problem for 2-bridge knots, since equivalent notations all produce a numerically identical fraction. The same cannot be said for the two parameters of Schubert's "normal form" diagrams.

Conway's notation, when further reduced to his finite continued fraction, is thus a miracle of precision for 2-bridge knots. It's a "complete invariant" for this particular class of knots.

For example, 1/(2+(1/-2))=-3 So in this sense Conway's notation is unique for 2-bridge (a/k/a “rational”) knots.

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Notation

Knot Theory

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