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).

# Perko Pair

## See also

Perko Move## Explore with Wolfram|Alpha

## References

Hoste, J.; Thistlethwaite, M.; and Weeks, J. "The First 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.

## Referenced on Wolfram|Alpha

Perko Pair## Cite this as:

Weisstein, Eric W. "Perko Pair." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/PerkoPair.html