flype

{{Short description|Operation on a knot}}

Image:Flype.svg

In the mathematical theory of knots, a flype is a kind of manipulation of knot and link diagrams

used in the Tait flyping conjecture.

It consists of twisting a part of a knot, a tangle T, by 180 degrees. Flype comes from a Scots word meaning to fold or to turn back ("as with a sock").{{citation

|last1 = Hoste

|first1 = Jim

|last2 = Thistlethwaite

|first2 = Morwen

|last3 = Weeks

|first3 = Jeff

|doi = 10.1007/BF03025227

|issue = 4

|journal = The Mathematical Intelligencer

|mr = 1646740

|pages = 33–48

|title = The first 1,701,936 knots

|url = http://www.math.harvard.edu/~ctm/home/text/class/harvard/101/05/html/home/pdf/first.pdf

|volume = 20

|year = 1998

|url-status = dead

|archiveurl = https://web.archive.org/web/20131215102511/http://www.math.harvard.edu/~ctm/home/text/class/harvard/101/05/html/home/pdf/first.pdf

|archivedate = 2013-12-15

}}. Tait used the term to mean, "a change of infinite complementary region").{{MathWorld|Flype|Flype}} Two reduced alternating diagrams of an alternating link can be transformed to each other using flypes. This is the Tait flyping conjecture, proven in 1991 by Morwen Thistlethwaite and William Menasco.{{MathWorld|TaitsKnotConjectures|Tait's Knot Conjectures}}