Perko pair

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In the mathematical theory of knots, the Perko pair, named after Kenneth Perko, is a pair of entries in classical knot tables that actually represent the same knot. In Rolfsen's knot table, this supposed pair of distinct knots is labeled 10161 and 10162. In 1974, while working to complete the Tait–Little knot tables of knots up to 10 crossings (dating from the late 19th century), Perko found the duplication in C. N. Little's table. This duplication had been missed by John Horton Conway several years before in his knot table and subsequently found its way into Rolfen's table.

The Perko Pair

10161

10162

[edit] References

  • Kenneth A. Perko Jr., On the classification of knots. Proc. Amer. Math. Soc. 45 (1974), 262--266.
  • Dale Rolfsen, Knots and Links (see Appendix C for the knot table), 1976, ISBN 0-914098-16-0
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