Conway's Knot Notation

A concise notation based on the concept of the tangle used by Conway (1967) to enumerate prime knots up to 11 crossings.

An algebraic knot containing no negative signs in its Conway knot notation is an alternating knot.

Conway's knot notation is implemented in the Wolfram Language as KnotData[knot, "ConwayNotation"]. Rolfsen (1976) gives a table that includes Conway's knot notation for prime knots on 10 or fewer crossings, as summarized in the table below.

REFERENCES:

Conway, J. H. "An Enumeration of Knots and Links, and Some of Their Algebraic Properties." In Computational Problems in Abstract Algebra (Ed. J. Leech). Oxford, England: Pergamon Press, pp. 329-358, 1967.

Rolfsen, D. "Table of Knots and Links." Appendix C in Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 280-287, 1976.