Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of flypes. The conjecture was proved by Menasco and Thistlethwaite (1991, 1993) using properties of the Jones polynomial. It allows all possible reduced alternating projections of a given alternating knot to be drawn.
Flyping Conjecture
See also
Alternating Knot, Flype, Reducible Crossing, Tait's Knot ConjecturesExplore with Wolfram|Alpha
References
Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp. 164-165, 1994.Hoste, J.; Thistlethwaite, M.; and Weeks, J. "The First
Knots." Math. Intell. 20, 33-48,
Fall 1998.Menasco, W. and Thistlethwaite, M. "The Tait Flyping
Conjecture." Bull. Amer. Math. Soc. 25, 403-412, 1991.Menasco,
W. and Thistlethwaite, M. "The Classification of Alternating Links." Ann.
Math. 138, 113-171, 1993.Stewart, I. The
Problems of Mathematics, 2nd ed. Oxford, England: Oxford University Press,
pp. 284-285, 1987.Referenced on Wolfram|Alpha
Flyping ConjectureCite this as:
Weisstein, Eric W. "Flyping Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FlypingConjecture.html