The proportion of links which are alternating tends exponentially to zero with increasing crossing number (Sundberg and Thistlethwaite 1998, Thistlethwaite 1998).
See alsoAlmost Alternating Link, Alternating Knot
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ReferencesHoste, J.; Thistlethwaite, M.; and Weeks, J. "The First ." 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.
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Cite this as:
Weisstein, Eric W. "Alternating Link." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AlternatingLink.html