Perko Pair

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). Rolfsen's 1976 first edition displays both and on p. 415 without noting their equivalence. The corrected 2003 printing retains the same pagination and both diagrams, but adds on p. 415, directly beneath , a parenthetical note that it is equivalent to (Rolfsen 1976, p. 415; Rolfsen 2003, p. 415). Although these knots are equivalent, their knot diagrams have different writhes (Hoste et al. 1998).