View source for Flype

{{Short description|Operation on a knot}}
[[Image:Flype.svg|170px|thumb|A flype consists of turning a tangle, '''T''', by 180 degrees.]]
In the [[knot theory|mathematical theory of knots]], a '''flype''' is a kind of manipulation of knot and [[knot diagram|link diagram]]s
used in the [[Tait conjectures|Tait flyping conjecture]].
It consists of twisting a part of a knot, a [[tangle (knot theory)|tangle]] '''T''', by 180 degrees. Flype comes from a [[Scots language|Scots]] word meaning ''to fold'' or ''to turn back'' ("as with a sock").<ref name="htw">{{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").</ref><ref>{{MathWorld|Flype|Flype}}</ref> 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]].<ref>{{MathWorld|TaitsKnotConjectures|Tait's Knot Conjectures}}</ref>
==See also==
* [[Reidemeister move]]s are another commonly studied kind of manipulation to knot diagrams.
==References==
{{reflist}}
{{Knot theory}}
[[Category:Knot operations]]
{{knottheory-stub}}