Alternating Link

A link which has a link diagram with alternating underpasses and overpasses.

The proportion of links which are alternating tends exponentially to zero with increasing crossing number (Sundberg and Thistlethwaite 1998, Thistlethwaite 1998).

See also

Almost Alternating Link, Alternating Knot

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Hoste, J.; Thistlethwaite, M.; and Weeks, J. "The First 1701936Knots." Math. Intell. 20, 33-48, Fall 1998.Menasco, W. and Thistlethwaite, M. "The Classification of Alternating Links." Ann. Math. 138, 113-171, 1993.Sundberg, C. and Thistlethwaite, M. "The Rate of Growth of the Number of Prime Alternating Links and Tangles." Pacific J. Math. 182, 329-358, 1998.Thistlethwaite, M. "On the Structure and Scarcity of Alternating Links and Tangles." J. Knot Th. Ramifications 7, 981-1004, 1998.

Referenced on Wolfram|Alpha

Alternating Link

Cite this as:

Weisstein, Eric W. "Alternating Link." From MathWorld--A Wolfram Web Resource.

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