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The Perko pair is the pair of knots 
and 
illustrated above. For many years, they were listed
as separate knots in Little (1885) and all similar tables, including the pictorial
enumeration of Rolfsen (1976, Appendix C). They were identified as identical by Perko
(1974), who found that they are related to one another by the so-called Perko
move (Perko 1974, Hoste et al. 1998). Although these knots are equivalent,
their diagrams have different writhes (Hoste et al.
1998).
Knots." Math. Intell. 20,
33-48, Fall 1998.Little, C. N. "On Knots, with a Census of
Order Ten." Trans. Connecticut Acad. Sci. 18, 374-378, 1885.Livingston,
C. Knot
Theory. Washington, DC: Math. Assoc. Amer., p. 10, 1993.Perko,
K. A. Jr. "On the Classification of Knots." Proc. Amer. Math. Soc. 45,
262-266, 1974.Rolfsen, D. "Table of Knots and Links." Appendix
C in Knots
and Links. Wilmington, DE: Publish or Perish Press, pp. 280-287, 1976.Weisstein, Eric W. "Perko Pair." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PerkoPair.html
