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Operation on a knot
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
Flype
All of the Tait conjectures have been solved, the most recent being the Flyping conjecture. Tait came up with his conjectures after his attempt to tabulate
Tait_conjectures
Simplest non-trivial closed knot with three crossings
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Trefoil_knot
Mathematical knot with crossing number 7
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
74_knot
Orientable surface whose boundary is a knot or link
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Seifert_surface
Group whose operation is a composition of braids
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Braid_group
Mathematical invariant of a knot or link
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Jones_polynomial
D2 by means of a sequence of certain simple moves called flypes. Also known as the Tait flyping conjecture. Morwen Thistlethwaite, Louis Kauffman and K
Alternating_knot
Spelling bee in the United States
champion, Navneeth Murali, took the first ever appeal win on the word "flype". Though he initially spelled the word as "flipe", it was accepted after
South_Asian_Spelling_Bee
Prime knot named for John Horton Conway
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Conway_knot
Type of mathematical link
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Hyperbolic_link
Knot invariant named after Cahit Arf
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Arf_invariant_of_a_knot
Unique knot with a crossing number of four
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Figure-eight knot (mathematics)
Figure-eight_knot_(mathematics)
Knot invariant
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Alexander_polynomial
Study of mathematical knots
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Knot_theory
Encyclopedic website dedicated to knot theory
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
The_Knot_Atlas
Three linked but pairwise separated rings
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Borromean_rings
Connected sum of two trefoil knots with opposite chirality
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Square_knot_(mathematics)
Knot which lies on the surface of a torus in 3-dimensional space
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Torus_knot
Kind of operation in knot theory
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Mutation_(knot_theory)
One of three types of isotopy-preserving local changes to a knot diagram
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Reidemeister_move
Polynomials arising in knot theory
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
HOMFLY_polynomial
Mathematical knot with crossing number 7
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
7_2_knot
Mathematician specializing in knot theory
D2 by means of a sequence of certain simple moves called flypes. Also known as the Tait flyping conjecture. (adapted from MathWorld—A Wolfram Web Resource
Morwen_Thistlethwaite
Non-trivial knot which cannot be written as the knot sum of two non-trivial knots
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Prime_knot
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Crosscap_number
Invariant of a knot diagram
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Writhe
Invariant of mathematical knots
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Khovanov_homology
Notation used to describe knots based on operations on tangles
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Conway_notation_(knot_theory)
How many times curves wind around each other
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Linking_number
Normalized hyperbolic volume of the complement of a hyperbolic knot
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Hyperbolic_volume
Interlinked multi-loop construction where cutting one loop frees all the others
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Brunnian_link
Motif with two doubly-interlinked loops
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Solomon's_knot
Knot that bounds an embedded disk in 4-space
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Slice_knot
Tangle numerator closure Reciprocal tangle Braid theory Braid group Band sum Flype Fox n-coloring Tricolorability Knot sum Reidemeister move elementary move
List_of_knot_theory_topics
Knot that is not equivalent to its mirror image
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Chiral_knot
Attempt to classify and tabulate all possible knots
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Knot_tabulation
Loop seen as a trivial knot
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Unknot
Generalization of knots in 3-dimensional Euclidean space
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Virtual_knot
Mathematical knot with crossing number 6
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Stevedore_knot_(mathematics)
Two-variable polynomial knot invariant
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Kauffman_polynomial
Fundamental group of a knot complement
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Knot_group
Determining whether a knot is the unknot
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Unknotting_problem
Mathematical tool for studying knots
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Skein_relation
Mathematical knot with crossing number 7
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
71_knot
are equivalent, prime or reduced. Knot moves or operations include the flype, Habiro move, Markov moves (I. conjugation and II. stabilization), pass
Knot_operation
Function of a knot that takes the same value for equivalent knots
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Knot_invariant
Simplest nontrivial knot link
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Hopf_link
Mathematical notation for describing the structure of knots
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Dowker–Thistlethwaite notation
Dowker–Thistlethwaite_notation
Minimum number of times a specific knot must be passed through itself to become untied
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Unknotting_number
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
2-bridge_knot
Integer-valued knot invariant; least number of crossings in a knot diagram
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Crossing_number_(knot_theory)
is connected. Menasco, along with Morwen Thistlethwaite proved the Tait flyping conjecture, which states that, given any two reduced alternating diagrams
William_Menasco
Operation combining two oriented knots
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Knot_(mathematics)
Family of mathematical knots
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Twist_knot
Type of mathematical knot
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
(−2,3,7)_pretzel_knot
Type of mathematical knot
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Satellite_knot
Two interlinked loops with five structural crossings
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Whitehead_link
Mathematical knot with crossing number 6
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
63_knot
Polynomial invariant of framed links
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Bracket_polynomial
Connected sum of two trefoil knots with same chirality
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Granny_knot_(mathematics)
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Bridge_number
Mathematical knot with crossing number 5
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Three-twist_knot
Complement of a knot in three-sphere
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Knot_complement
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Knot_polynomial
Link formed from a finite number of twisted sections
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Pretzel_link
Type of invariant in Knot theory
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Finite_type_invariant
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
List_of_prime_knots
Mathematical knot with crossing number 5
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Cinquefoil_knot
Property in knot theory
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Tricolorability
Invariant of framed knots
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Self-linking_number
Mathematical knot
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Fibered_knot
Collection of knots that do not intersect, but may be linked
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Link_(knot_theory)
Foot-launched powered hang glider
Wasp, Flylight Doodle Bug, Raven, X1, Zenon, Airtime Explorer, Fillo, and Flyped. La Fédération Aéronautique Internationale (FAI) is the international standard-setting
Powered_hang_glider
Smallest number of edges of an equivalent polygonal path for a knot
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Stick_number
Scottish mathematical physicist (1831–1901)
All of the Tait conjectures have been solved, the most recent being the Flyping conjecture, proved by Morwen Thistlethwaite and William Menasco in 1991
Peter_Guthrie_Tait
Mathematical knot with crossing number 6
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
62_knot
Knot that can't be tied in a string of constant diameter
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Wild_knot
Analog of the knot group
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Link_group
Link of three loops with ten crossings
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
L10a140_link
Every knot or link can be represented as a closed braid
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Alexander's_theorem
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
List of mathematical knots and links
List_of_mathematical_knots_and_links
Prime knot with crossing number 10
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Perko_pair
Type of mathematical knot
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Ribbon_knot
Link that consists of finitely many unlinked unknots
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Unlink
Concept in knot theory
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Conway_sphere
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Tunnel_number
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Invertible_knot
Flat woven decorative knot
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Carrick_mat
Class of mathematical knot with special properties
Alexander–Briggs notation Conway notation Dowker–Thistlethwaite notation Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem
Berge_knot
FLYPE
FLYPE
FLYPE
FLYPE
Boy/Male
Tamil
Arivarasu | அரிவாராஸூÂ
King of wisdom
Boy/Male
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Polite; Innocent; Divine; Honesty; Virtuous; Healthy; Pure
Boy/Male
Tamil
Devine
Girl/Female
Indian
Woman.
Male
English
 Medieval English form of Anglo-Saxon Eoforwin, ERWIN means "boar friend." Compare with another form of Erwin.
Girl/Female
Hindu, Indian, Marathi, Sanskrit, Telugu
Immovable; Fixed; Quiet
Girl/Female
Arabic, Muslim
To Tend
Girl/Female
Gujarati, Hindu, Indian, Sikh
Happiness and Joy
Boy/Male
Tamil
Mighty
Girl/Female
Norse
Thor's fighter.
FLYPE
FLYPE
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