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).

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.