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).
Alternating Link
See also
Almost Alternating Link, Alternating KnotExplore with Wolfram|Alpha
References
Hoste, 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.Referenced on Wolfram|Alpha
Alternating LinkCite this as:
Weisstein, Eric W. "Alternating Link." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AlternatingLink.html