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UNKNOTTING NUMBER

  • Unknotting number
  • Minimum number of times a specific knot must be passed through itself to become untied

    unknotting numbers for the first few knots: Trefoil knot unknotting number 1 Figure-eight knot unknotting number 1 Cinquefoil knot unknotting number 2

    Unknotting number

    Unknotting number

    Unknotting_number

  • Unknotting
  • Topics referred to by the same term

    Unknotting may refer to: Unknotting number, the minimum number of times the knot must be passed through itself to untie it Unknotting problem, a mathematical

    Unknotting

    Unknotting

  • Unknotting problem
  • Determining whether a knot is the unknot

    showed that the unknotting problem is in the complexity class NP. Hara, Tani & Yamamoto (2005) claimed the weaker result that unknotting is in AM ∩ co-AM;

    Unknotting problem

    Unknotting problem

    Unknotting_problem

  • Crossing number (knot theory)
  • Integer-valued knot invariant; least number of crossings in a knot diagram

    equal to crossing number. Other numerical knot invariants include the bridge number, linking number, stick number, and unknotting number. Tait, P. G. (1898)

    Crossing number (knot theory)

    Crossing number (knot theory)

    Crossing_number_(knot_theory)

  • 71 knot
  • Mathematical knot with crossing number 7

    construct the simplest known counterexample to the conjecture that the unknotting number is additive under connected sum. The 71 knot is invertible but not

    71 knot

    71 knot

    71_knot

  • Unknot
  • Loop seen as a trivial knot

    Embedding of the circle in three dimensional Euclidean space Unknotting number – Minimum number of times a specific knot must be passed through itself to

    Unknot

    Unknot

    Unknot

  • Bridge number
  • bridge number of K is one less than the sum of the bridge numbers of K1 and K2. Crossing number Linking number Stick number Unknotting number Adams, Colin

    Bridge number

    Bridge number

    Bridge_number

  • Twist knot
  • Family of mathematical knots

    half-twists (72 knot) Six half-twists (81 knot) All twist knots have unknotting number one, since the knot can be untied by unlinking the two ends. Every

    Twist knot

    Twist knot

    Twist_knot

  • Susan Hermiller
  • American mathematician

    unknotting number of a knot was not viable. In 2025, the pair gave a counterexample to another long-standing conjecture, showing that the unknotting number

    Susan Hermiller

    Susan_Hermiller

  • Linking number
  • How many times curves wind around each other

    single curve is regular homotopic to a standard circle (any knot can be unknotted if the curve is allowed to pass through itself). The fact that it is homotopic

    Linking number

    Linking number

    Linking_number

  • Alexander polynomial
  • Knot invariant

    150. Kawauchi credits this result to Kondo, H. (1979), "Knots of unknotting number 1 and their Alexander polynomials", Osaka J. Math. 16: 551-559, and

    Alexander polynomial

    Alexander_polynomial

  • Open knot theory
  • Mathematical theory

    provides a measure of complexity of an open curve similar to the unknotting number. Virtual knots are another generalization of knot diagrams. Whereas

    Open knot theory

    Open knot theory

    Open_knot_theory

  • Martin Scharlemann
  • American mathematician

    He gave the first proof of the classical theorem that knots with unknotting number one are prime. He used hard combinatorial arguments for this. Simpler

    Martin Scharlemann

    Martin_Scharlemann

  • Conway sphere
  • Concept in knot theory

    Conway spheres. Gordon, Cameron McA.; Luecke, John (2006). "Knots with unknotting number 1 and essential Conway spheres". Algebraic & Geometric Topology. 6

    Conway sphere

    Conway sphere

    Conway_sphere

  • List of knot theory topics
  • conjectures Temperley–Lieb algebra Thurston–Bennequin number Tricolorability Unknotting number Unknotting problem Volume conjecture Schubert's theorem Conway's

    List of knot theory topics

    List_of_knot_theory_topics

  • List of unsolved problems in mathematics
  • last of Ravenel's conjectures in stable homotopy theory to be resolved. Unknotting problem: can unknots be recognized in polynomial time? Volume conjecture

    List of unsolved problems in mathematics

    List_of_unsolved_problems_in_mathematics

  • Knots Unravelled
  • 2011 knot theory book by Meike Akveld and Andrew Jobbings

    crossing number of a knot, the minimum number of crossings in its diagrams. Chapter four discusses another invariant, the unknotting number, the minimum

    Knots Unravelled

    Knots_Unravelled

  • Human knot
  • Physical team-building activity

    Not all human knots are solvable, as can be shown in knot theory (see unknotting problem), and can remain knots or may end up as two or more circles. An

    Human knot

    Human knot

    Human_knot

  • Borromean rings
  • Three linked but pairwise separated rings

    and cannot be separated from each other, but that break apart into two unknotted and unlinked loops when any one of the three is cut or removed. Most commonly

    Borromean rings

    Borromean rings

    Borromean_rings

  • Figure-eight knot (mathematics)
  • Unique knot with a crossing number of four

    the unique knot with a crossing number of four. This makes it the knot with the third-smallest possible crossing number, after the unknot and the trefoil

    Figure-eight knot (mathematics)

    Figure-eight knot (mathematics)

    Figure-eight_knot_(mathematics)

  • Torus knot
  • Knot which lies on the surface of a torus in 3-dimensional space

    a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies on the surface

    Torus knot

    Torus knot

    Torus_knot

  • Stick number
  • Smallest number of edges of an equivalent polygonal path for a knot

    mathematical theory of knots, the stick number is a knot invariant that intuitively gives the smallest number of straight "sticks" stuck end to end needed

    Stick number

    Stick number

    Stick_number

  • Reidemeister move
  • One of three types of isotopy-preserving local changes to a knot diagram

    MR 2170571 Hass, Joel; Lagarias, Jeffrey C. (2001), "The number of Reidemeister moves needed for unknotting", Journal of the American Mathematical Society, 14

    Reidemeister move

    Reidemeister move

    Reidemeister_move

  • Stevedore knot (mathematics)
  • Mathematical knot with crossing number 6

    knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot. The stevedore knot is

    Stevedore knot (mathematics)

    Stevedore knot (mathematics)

    Stevedore_knot_(mathematics)

  • Cinquefoil knot
  • Mathematical knot with crossing number 5

    Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other being the three-twist knot. It is listed as the 51 knot

    Cinquefoil knot

    Cinquefoil knot

    Cinquefoil_knot

  • 7 2 knot
  • Mathematical knot with crossing number 7

    the five-twist knot, or the 72, is one of seven prime knots with crossing number seven. It is the fifth twist knot. Its Alexander polynomial is Δ ( t ) =

    7 2 knot

    7 2 knot

    7_2_knot

  • Link group
  • Analog of the knot group

    move through regular homotopy (homotopy through immersions), knotting or unknotting itself, but is not allowed to move through other components. This is a

    Link group

    Link_group

  • Three-twist knot
  • Mathematical knot with crossing number 5

    in the Alexander-Briggs notation, and is one of two knots with crossing number five, the other being the cinquefoil knot. The 52 knot can be represented

    Three-twist knot

    Three-twist knot

    Three-twist_knot

  • Tait conjectures
  • been removed. Tait conjectured that in certain circumstances, crossing number was a knot invariant, specifically: Any reduced diagram of an alternating

    Tait conjectures

    Tait_conjectures

  • Trefoil knot
  • Simplest non-trivial closed knot with three crossings

    trefoil is the first nontrivial knot, and is the only knot with crossing number three. It is a prime knot, and is listed as 31 in the Alexander-Briggs notation

    Trefoil knot

    Trefoil knot

    Trefoil_knot

  • Perko pair
  • Prime knot with crossing number 10

    they are the same. The Perko pair 10161 10162 (in Rolfsen's original numbering) The Perko pair was correctly illustrated and explained on the first page

    Perko pair

    Perko pair

    Perko_pair

  • Topoisomerase
  • Class of enzymes

    (Fig. 3). The range of reactions includes: DNA supercoil relaxation, unknotting of single-stranded circles, and decatenation, provided at least one partner

    Topoisomerase

    Topoisomerase

  • Braid group
  • Group whose operation is a composition of braids

    possibly intertwined union of possibly knotted loops in three dimensions. The number of components of the link can be anything from 1 to n, depending on the

    Braid group

    Braid group

    Braid_group

  • Knot (mathematics)
  • Embedding of the circle in three dimensional Euclidean space

    an embedding of the graph with the property that any single cycle is unknotted. The graphs that have linkless embeddings have a forbidden graph characterization

    Knot (mathematics)

    Knot (mathematics)

    Knot_(mathematics)

  • Knot theory
  • Study of mathematical knots

    is (Hass 1998). The special case of recognizing the unknot, called the unknotting problem, is of particular interest (Hoste 2005). In February 2021 Marc

    Knot theory

    Knot theory

    Knot_theory

  • Tunnel number
  • mathematics, the tunnel number of a knot, as first defined by Bradd Clark, is a knot invariant, given by the minimal number of arcs (called tunnels)

    Tunnel number

    Tunnel_number

  • Tree-like curve
  • Type of planar curve with tree-like structure

    sums of figure-eight curves. Each figure-eight is unknotted and their connected sum remains unknotted. Random curves with few crossings are likely to be

    Tree-like curve

    Tree-like curve

    Tree-like_curve

  • Writhe
  • Invariant of a knot diagram

    an oriented link diagram. The writhe is the total number of positive crossings minus the total number of negative crossings. A direction is assigned to

    Writhe

    Writhe

  • Quasi-polynomial time
  • Computational complexity class

    vertices, announced in 2015 and updated in 2017 by László Babai. The unknotting problem, recognizing whether a knot diagram describes the unknot, announced

    Quasi-polynomial time

    Quasi-polynomial_time

  • Train Dreams
  • 2011 novella by Denis Johnson

    and breaking her back on rocks down by the river. Before drowning, she unknotted her bodice to allow Kate to crawl away and escape. Thereafter, Grainier

    Train Dreams

    Train_Dreams

  • Khajuraho Group of Monuments
  • Historic temples in Madhya Pradesh, India

    washing their hair, playing games, dancing, and endlessly knotting and unknotting their girdles. ... Beside the heavenly nymphs are serried ranks of griffins

    Khajuraho Group of Monuments

    Khajuraho Group of Monuments

    Khajuraho_Group_of_Monuments

  • Alternating knot
  • alternating if it has an alternating diagram. Many of the knots with crossing number less than 10 are alternating. This fact and useful properties of alternating

    Alternating knot

    Alternating knot

    Alternating_knot

  • 74 knot
  • Mathematical knot with crossing number 7

    Crosscap no. 3 Crossing no. 7 Genus 1 Hyperbolic volume 5.13794 Stick no. 9 Unknotting no. 2 Conway notation [313] A–B notation 74 Dowker notation 6, 10, 12

    74 knot

    74 knot

    74_knot

  • 2-bridge knot
  • Type of knot in knot theory

    Bridge number 2 In the mathematical field of knot theory, a 2-bridge knot is a knot which can be regular isotoped so that the natural height function given

    2-bridge knot

    2-bridge_knot

  • 62 knot
  • Mathematical knot with crossing number 6

    In knot theory, the 62 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 63 knot. This knot is sometimes

    62 knot

    62 knot

    62_knot

  • Whitehead manifold
  • Open 3-manifold that is contractible but not homeomorphic to R3

    {\displaystyle S^{3},} the three-dimensional sphere. Now find a compact unknotted solid torus T 1 {\displaystyle T_{1}} inside the sphere. (A solid torus

    Whitehead manifold

    Whitehead manifold

    Whitehead_manifold

  • Sigmund Freud
  • Austrian neurologist and founder of psychoanalysis (1856–1939)

    they were all harboring memories of early abuse ... and cured them by unknotting their repression." Crews sees Freud as having anticipated the recovered

    Sigmund Freud

    Sigmund Freud

    Sigmund_Freud

  • Joel Hass
  • American mathematician

    Pippenger, he proved that the unknotting problem is in NP. With Lagarias, he gave an exponential upper bound on the number of Reidemeister moves needed

    Joel Hass

    Joel Hass

    Joel_Hass

  • Self-linking number
  • Invariant of framed knots

    In knot theory, the self-linking number is an invariant of framed knots. It is related to the linking number of curves. A framing of a knot is a choice

    Self-linking number

    Self-linking_number

  • Crosscap number
  • In the mathematical field of knot theory, the crosscap number of a knot K is the minimum of C ( K ) ≡ 1 − χ ( S ) , {\displaystyle C(K)\equiv 1-\chi (S)

    Crosscap number

    Crosscap_number

  • Force spectroscopy
  • Set of scientific techniques

    generation (F1-ATPase), DNA replication and transcription (polymerases), DNA unknotting and unwinding (topoisomerases and helicases). As a single-molecule technique

    Force spectroscopy

    Force_spectroscopy

  • Knot tabulation
  • Attempt to classify and tabulate all possible knots

    a matter of days. Knot theory Knot (mathematics) List of prime knots Unknotting problem Hoste, Jim; Thistlethwaite, Morwen; Weeks, Jeff (1998), "The first

    Knot tabulation

    Knot tabulation

    Knot_tabulation

  • Depictions of nudity
  • Visual representations of the nude human form

    washing their hair, playing games, dancing, and endlessly knotting and unknotting their girdles....Beside the heavenly nymphs are serried ranks of griffins

    Depictions of nudity

    Depictions of nudity

    Depictions_of_nudity

  • Whitehead link
  • Two interlinked loops with five structural crossings

    towards the linking number. Because the remaining crossings have equal numbers of under and over crossings on each loop, its linking number is 0. It is not

    Whitehead link

    Whitehead link

    Whitehead_link

  • History of knot theory
  • invariants. In the 1980s John Horton Conway discovered a procedure for unknotting knots gradually known as Conway notation. In 1992, the Journal of Knot

    History of knot theory

    History of knot theory

    History_of_knot_theory

  • Möbius strip
  • Non-orientable surface with one edge

    of the Möbius strip, it has a different shape from a circle, but it is unknotted, and therefore the whole strip can be stretched without crossing itself

    Möbius strip

    Möbius strip

    Möbius_strip

  • A Moon Shaped Pool
  • 2016 studio album by Radiohead

    of car crash of the soul, is palpable. The music here feels loose and unknotted, broken open in the way you can only be after a tragedy." Pitchfork later

    A Moon Shaped Pool

    A_Moon_Shaped_Pool

  • Knot invariant
  • Function of a knot that takes the same value for equivalent knots

    the crossing number, which is the minimum number of crossings for any diagram of the knot, and the bridge number, which is the minimum number of bridges

    Knot invariant

    Knot invariant

    Knot_invariant

  • Chromatin
  • Complex of DNA and protein in eukaryotic cells

    Goundaroulis D, Stasiak A (2018). "Chromatin Loop Extrusion and Chromatin Unknotting". Polymers. 10 (10): 1126–1137. doi:10.3390/polym10101126. PMC 6403842

    Chromatin

    Chromatin

  • Invertible knot
  • now known almost all knots are non-invertible. All knots with crossing number of 7 or less are known to be invertible. No general method is known that

    Invertible knot

    Invertible_knot

  • 63 knot
  • Mathematical knot with crossing number 6

    In knot theory, the 63 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 62 knot. It is alternating

    63 knot

    63 knot

    63_knot

  • Chiral knot
  • Knot that is not equivalent to its mirror image

    crossings and conjectured that all amphichiral knots had even crossing number. Mary Gertrude Haseman found all 12-crossing and many 14-crossing amphichiral

    Chiral knot

    Chiral_knot

  • Marc Lackenby
  • and earned his Ph.D. in 1997, with a dissertation on Dehn Surgery and Unknotting Operations supervised by W. B. R. Lickorish. After positions as Miller

    Marc Lackenby

    Marc Lackenby

    Marc_Lackenby

  • Slice knot
  • Knot that bounds an embedded disk in 4-space

    Up to this crossing number there are no topologically slice knots which are not smoothly slice. Starting with crossing number 11 there is such an example

    Slice knot

    Slice knot

    Slice_knot

  • Unlink
  • Link that consists of finitely many unlinked unknots

    Whitehead link and Borromean rings are such examples for n = 2, 3. Linking number Kanenobu, Taizo (1986), "Hyperbolic links with Brunnian properties", Journal

    Unlink

    Unlink

    Unlink

  • Jones polynomial
  • Mathematical invariant of a knot or link

    writhe of a diagram is the number of positive crossings ( L + {\displaystyle L_{+}} in the figure below) minus the number of negative crossings ( L −

    Jones polynomial

    Jones_polynomial

  • Saif al-Islam Gaddafi
  • Libyan political figure (1972–2026)

    May 2025. Retrieved 11 August 2021. Thomas, Landon (28 February 2010). "Unknotting Father's Reins in Hope of "Reinventing" Libya". The New York Times. Archived

    Saif al-Islam Gaddafi

    Saif al-Islam Gaddafi

    Saif_al-Islam_Gaddafi

  • Mattress
  • Large soft mat for lying on to sleep

    effect of the unit is designed to conform to body shape. LFK coils are an unknotted offset coil with a cylindrical or columnar shape. Continuous coils (the

    Mattress

    Mattress

    Mattress

  • Möbius energy
  • Particular knot energy

    problem really is. The special case of recognizing the unknot, called the unknotting problem, is of particular interest. We shall picture a knot by a smooth

    Möbius energy

    Möbius energy

    Möbius_energy

  • Disentanglement puzzle
  • Simple mechanical puzzles using topology

    puzzle by the Jakun indigenous tribe in Malaysia Human knot Tangloids Unknotting problem Unlink Horak, Matthew (2006). "Disentangling Topological Puzzles

    Disentanglement puzzle

    Disentanglement puzzle

    Disentanglement_puzzle

  • Multiverse (DC Comics)
  • Multiverse used by DC Comics

    is recreated by the Hands as an Omniverse. The timeline of the DCU is "unknotted", meaning that every version of history throughout the existence of the

    Multiverse (DC Comics)

    Multiverse_(DC_Comics)

  • List of mathematical knots and links
  • q)-torus knot - a special kind of knot that lies on the surface of an unknotted torus in R3 Square knot (mathematics) - a composite knot obtained by taking

    List of mathematical knots and links

    List of mathematical knots and links

    List_of_mathematical_knots_and_links

  • Mutation (knot theory)
  • Kind of operation in knot theory

    called a mutant of K. Mutants can be difficult to distinguish as they have a number of the same invariants. They have the same hyperbolic volume (by a result

    Mutation (knot theory)

    Mutation (knot theory)

    Mutation_(knot_theory)

  • Prime knot
  • Non-trivial knot which cannot be written as the knot sum of two non-trivial knots

    simplest non-torus knot. For any positive integer n, there are a finite number of prime knots with n crossings. The first few values for exclusively prime

    Prime knot

    Prime knot

    Prime_knot

  • Arf invariant of a knot
  • Knot invariant named after Cahit Arf

    the homology group H1(F, Z/2Z) has a quadratic form whose value is the number of full twists mod 2 in a neighborhood of an embedded circle representing

    Arf invariant of a knot

    Arf_invariant_of_a_knot

  • Pretzel link
  • Link formed from a finite number of twisted sections

    knots, a pretzel link is a special kind of link. It consists of a finite number of tangles made of two intertwined circular helices. The tangles are connected

    Pretzel link

    Pretzel link

    Pretzel_link

  • Conway notation (knot theory)
  • Notation used to describe knots based on operations on tangles

    crossings are denoted by the number of crossings, or if there are only negative crossings it is denoted by a negative number. If the arcs are not crossed

    Conway notation (knot theory)

    Conway notation (knot theory)

    Conway_notation_(knot_theory)

  • Hopf link
  • Simplest nontrivial knot link

    Depending on the relative orientations of the two components the linking number of the Hopf link is ±1. The Hopf link is a (2,2)-torus link with the braid

    Hopf link

    Hopf link

    Hopf_link

  • Hydrodynamical helicity
  • Aspect of Eulerian fluid dynamics

    other three are energy, momentum and angular momentum. For two linked unknotted vortex tubes having circulations κ 1 {\displaystyle \kappa _{1}} and κ

    Hydrodynamical helicity

    Hydrodynamical_helicity

  • Khovanov homology
  • Invariant of mathematical knots

    n_{-}} denotes the number of left-handed crossings in the chosen diagram for D {\displaystyle D} , and n + {\displaystyle n_{+}} the number of right-handed

    Khovanov homology

    Khovanov_homology

  • Dowker–Thistlethwaite notation
  • Mathematical notation for describing the structure of knots

    labelled twice), with the following modification: if the label is an even number and the strand followed crosses over at the crossing, then change the sign

    Dowker–Thistlethwaite notation

    Dowker–Thistlethwaite notation

    Dowker–Thistlethwaite_notation

  • Tricolorability
  • Property in knot theory

    always tricolorable. A way to strengthen the invariant is to count the number of possible 3-colorings. In this case, the rule that at least two colors

    Tricolorability

    Tricolorability

    Tricolorability

  • Seifert surface
  • Orientable surface whose boundary is a knot or link

    {\displaystyle V=(v(i,j))} has v ( i , j ) {\displaystyle v(i,j)} the linking number in Euclidean 3-space (or in the 3-sphere) of ai and the "pushoff" of aj

    Seifert surface

    Seifert surface

    Seifert_surface

  • Link (knot theory)
  • Collection of knots that do not intersect, but may be linked

    constitute the simplest such link. The notion of a link can be generalized in a number of ways. Frequently the word link is used to describe any submanifold of

    Link (knot theory)

    Link (knot theory)

    Link_(knot_theory)

  • Donna Troy
  • DC Comics superhero

    Amazon – was re-established as her true origin after the timeline was "unknotted" by Wonder Woman. Titans Annual (2025) retells Donna's memories, which

    Donna Troy

    Donna_Troy

  • Knotted protein
  • Proteins with backbone entangled in a knot

    ability of the protein to resist unknotting. A deep knot is preserved even though the removal of a considerable number of residues from either end does

    Knotted protein

    Knotted protein

    Knotted_protein

  • Knot polynomial
  • polynomial. Alexander–Briggs notation organizes knots by their crossing number. Alexander polynomials and Conway polynomials can not recognize the difference

    Knot polynomial

    Knot polynomial

    Knot_polynomial

  • Brunnian link
  • Interlinked multi-loop construction where cutting one loop frees all the others

    However for every number three or above, there are an infinite number of links with the Brunnian property containing that number of loops. Here are some

    Brunnian link

    Brunnian link

    Brunnian_link

  • 3-manifold
  • Mathematical space

    coefficients. Furthermore, each component of the link can be assumed to be unknotted. Friedhelm Waldhausen's theorems on topological rigidity say that certain

    3-manifold

    3-manifold

    3-manifold

  • Square knot (mathematics)
  • Connected sum of two trefoil knots with opposite chirality

    its own mirror image. The crossing number of a square knot is six, which is the smallest possible crossing number for a composite knot. The Alexander

    Square knot (mathematics)

    Square knot (mathematics)

    Square_knot_(mathematics)

  • Granny knot (mathematics)
  • Connected sum of two trefoil knots with same chirality

    result is a square knot. The crossing number of a granny knot is six, which is the smallest possible crossing number for a composite knot. Unlike the square

    Granny knot (mathematics)

    Granny knot (mathematics)

    Granny_knot_(mathematics)

  • The Grinning Man (Jonathan Creek)
  • Episode of Jonathan Creek

    fantasy in a way that defies belief and interest. It is a dull confusion of unknotted loose ends that breaks its own rules, suspends common sense and dumps

    The Grinning Man (Jonathan Creek)

    The_Grinning_Man_(Jonathan_Creek)

  • Knot operation
  • a knot move or operation is a change or changes which preserve crossing number. Operations are used to investigate whether knots are equivalent, prime

    Knot operation

    Knot_operation

  • Glossary of cellular and molecular biology (M–Z)
  • between its relaxed and supercoiled, linked and unlinked, and knotted and unknotted forms without changing the sequence or overall chemical composition, such

    Glossary of cellular and molecular biology (M–Z)

    Glossary_of_cellular_and_molecular_biology_(M–Z)

  • Hyperbolic volume
  • Normalized hyperbolic volume of the complement of a hyperbolic knot

    its complete hyperbolic metric. The volume is necessarily a finite real number, and is a topological invariant of the link. As a link invariant, it was

    Hyperbolic volume

    Hyperbolic volume

    Hyperbolic_volume

  • Molecular knot
  • Molecule whose structure resembles a knot

    contains knotted subchains even though their backbone chain as a whole is unknotted and does not contain completely knotted structures that are easily detectable

    Molecular knot

    Molecular knot

    Molecular_knot

  • Linkless embedding
  • Embedding a graph in 3D space with no cycles interlinked

    is equivalent in complexity to unknotting problem, the problem of testing whether a single curve in space is unknotted. Testing unknottedness (and therefore

    Linkless embedding

    Linkless_embedding

  • Ribbon knot
  • Type of mathematical knot

    ribbon? Lisca (2007) showed that the conjecture is true for knots of bridge number two. Greene & Jabuka (2011) showed it to be true for three-stranded pretzel

    Ribbon knot

    Ribbon knot

    Ribbon_knot

  • Fibered knot
  • Mathematical knot

    2 q + 1 ) + q t − 1 {\displaystyle qt-(2q+1)+qt^{-1}} , where q is the number of half-twists. In particular the stevedore knot is not fibered. Fibered

    Fibered knot

    Fibered knot

    Fibered_knot

AI & ChatGPT searchs for online references containing UNKNOTTING NUMBER

UNKNOTTING NUMBER

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UNKNOTTING NUMBER

  • IGNÁC
  • Male

    Hungarian

    IGNÁC

    Czech and Hungarian form of Latin Ignatius, possibly IGNÁC means "unknowing."

    IGNÁC

  • IGNAC
  • Male

    Slovene

    IGNAC

    Short form of Slovene Ignacij, possibly IGNAC means "unknowing."

    IGNAC

  • IGNACY
  • Male

    Polish

    IGNACY

    Polish form of Latin Ignatius, possibly IGNACY means "unknowing."

    IGNACY

  • NACIO
  • Male

    Spanish

    NACIO

    Pet form of Spanish Ignacio, possibly NACIO means "unknowing."

    NACIO

  • Male
  • Surname or Lastname

    English

    Male

    English : nickname for a virile man, from Middle English male ‘masculine’ (Old French masle, madle, Latin masculus).Belgian (van Male) : habitational name from any of a number of places in Flanders named Male.

    Male

  • NACHO
  • Male

    Spanish

    NACHO

    Pet form of Spanish Ignacio, possibly NACHO means "unknowing."

    NACHO

  • INÁCIO
  • Male

    Portuguese

    INÁCIO

    Portuguese form of Latin Ignatius, possibly INÁCIO means "unknowing."

    INÁCIO

  • Lupton
  • Surname or Lastname

    English

    Lupton

    English : habitational name from a place in Cumbria (Westmorland). The place name is recorded in Domesday Book as Lupetun, and probably derives from an Old English personal name Hluppa (of uncertain origin) + Old English tūn ‘enclosure’, ‘settlement’.The name was brought to America by John Lupton, who sailed from Gravesend, England, on the Primrose in 1635, and is recorded in VA three years later. On 24 October 1635 Davie Lupton set off on the Constance bound for VA, but there is no record of his arrival in the New World. A Christopher Lupton is recorded in Suffolk Co., Long Island, NY, c.1635, and a large number of Luptons in NC descend from him. An American family of the name settled in the area of Winchester, VA, in the mid18th century; they can be traced back to Martin Lupton, who was married in 1630 in the parish of Rothwell, Yorkshire, England.

    Lupton

  • Mars
  • Surname or Lastname

    English

    Mars

    English : variant of Marsh.French : habitational name from places so named in Ardèche, Ardennes, Gard, Loire, Nièvre, and Meurthe-et-Moselle, from the Latin personal name Marcius, used adjectivally.French : from the personal name Meard, Mard, Mart, vernacular forms of the saint’s name Médard. Morlet notes that there are a number of places called Saint-Mars, formerly recorded in Latin as Sanctus Medardus.French : from the name of the month, mars ‘ March’, denoting seed sown in March, and hence a metonymic name for an arable grower.French (De Mars) : habitational name from Mars in the Ardennes.Dutch : from a short form of the personal name Marsilius.

    Mars

  • IGNAZIO
  • Male

    Italian

    IGNAZIO

    Italian form of Latin Ignatius, possibly IGNAZIO means "unknowing."

    IGNAZIO

  • Mark
  • Surname or Lastname

    English and Dutch

    Mark

    English and Dutch : from Latin Marcus, the personal name of St. Mark the Evangelist, author of the second Gospel. The name was borne also by a number of other early Christian saints. Marcus was an old Roman name, of uncertain (possibly non-Italic) etymology; it may have some connection with the name of the war god Mars. Compare Martin. The personal name was not as popular in England in the Middle Ages as it was on the Continent, especially in Italy, where the evangelist became the patron of Venice and the Venetian Republic, and was allegedly buried at Aquileia. As an American family name, this has absorbed cognate and similar names from other European languages, including Greek Markos and Slavic Marek.English, German, and Dutch (van der Mark) : topographic name for someone who lived on a boundary between two districts, from Middle English merke, Middle High German marc, Middle Dutch marke, merke, all meaning ‘borderland’. The German term also denotes an area of fenced-off land (see Marker 5) and, like the English word, is embodied in various place names which have given rise to habitational names.English (of Norman origin) : habitational name from Marck, Pas-de-Calais.German : from Marko, a short form of any of the Germanic compound personal names formed with mark ‘borderland’ as the first element, for example Markwardt.Americanization or shortened form of any of several like-sounding Jewish or Slavic surnames (see for example Markow, Markowitz, Markovich).Irish (northeastern Ulster) : probably a short form of Markey (when not of English origin).

    Mark

  • Mainwaring
  • Surname or Lastname

    English (of Norman origin)

    Mainwaring

    English (of Norman origin) : habitational name from a lost place, of uncertain location, named in Anglo-Norman French as mesnil Warin ‘domain of Warin’ (see Waring). The surname has had a large number of variant spellings; it is normally pronounced ‘Mannering’.

    Mainwaring

  • John
  • Surname or Lastname

    English, Welsh, German, etc.

    John

    English, Welsh, German, etc. : ultimately from the Hebrew personal name yọ̄hānān ‘Jehovah has favored (me with a son)’ or ‘may Jehovah favor (this child)’. This personal name was adopted into Latin (via Greek) as Johannes, and has enjoyed enormous popularity in Europe throughout the Christian era, being given in honor of St. John the Baptist, precursor of Christ, and of St. John the Evangelist, author of the fourth gospel, as well as others of the nearly one thousand other Christian saints of the name. Some of the principal forms of the personal name in other European languages are Welsh Ieuan, Evan, Siôn, and Ioan; Scottish Ia(i)n; Irish Séan; German Johann, Johannes, Hans; Dutch Jan; French Jean; Italian Giovanni, Gianni, Ianni; Spanish Juan; Portuguese João; Greek Iōannēs (vernacular Yannis); Czech Jan; Russian Ivan. Polish has surnames both from the western Slavic form Jan and from the eastern Slavic form Iwan. There were a number of different forms of the name in Middle English, including Jan(e), a male name (see Jane); Jen (see Jenkin); Jon(e) (see Jones); and Han(n) (see Hann). There were also various Middle English feminine versions of this name (e.g. Joan, Jehan), and some of these were indistinguishable from masculine forms. The distinction on grounds of gender between John and Joan was not firmly established in English until the 17th century. It was even later that Jean and Jane were specialized as specifically feminine names in English; bearers of these surnames and their derivatives are more likely to derive them from a male ancestor than a female. As a surname in the British Isles, John is particularly frequent in Wales, where it is a late formation representing Welsh Siôn rather than the older form Ieuan (which gave rise to the surname Evan). As an American family name this form has absorbed various cognates from continental European languages. (For forms, see Hanks and Hodges 1988.)

    John

  • January
  • Surname or Lastname

    Americanized form of the Latin personal name Januarius or its Italian derivative Gennaro, which was borne by a number of early Christian saints, most famously a 3rd-century bishop of Benevento who became the patron of Naples.English

    January

    Americanized form of the Latin personal name Januarius or its Italian derivative Gennaro, which was borne by a number of early Christian saints, most famously a 3rd-century bishop of Benevento who became the patron of Naples.English : altered form of Janeway.In New England, a translation of French Janvier.

    January

  • IGNATZ
  • Male

    German

    IGNATZ

    German form of Latin Ignatius, possibly IGNATZ means "unknowing." It is interesting to note that the word Nazi originated as a short form of Ignatz and was used colloquially as a byname for a foolish or awkward person.

    IGNATZ

  • Martineau
  • Surname or Lastname

    French (western)

    Martineau

    French (western) : from a pet form of Martin 1.English : habitational name from Martineau in France. The name was also taken to England by Huguenot refugees in the 17th century (see below).Harriet Martineau (1802–76), the English writer, was the daughter of a Norwich manufacturer. She was descended from a family of French Huguenots who owned land around Poitou and Touraine in the 15th century. They included a number of surgeons in the 17th century. In the 19th century a branch of the family was firmly established in Birmingham, England; others went to North America.

    Martineau

  • IGNACIJ
  • Male

    Slovene

    IGNACIJ

    Slovene form of Latin Ignatius, possibly IGNACIJ means "unknowing."

    IGNACIJ

  • IGNACIO
  • Male

    Spanish

    IGNACIO

    Spanish form of Latin Ignatius, possibly IGNACIO means "unknowing."

    IGNACIO

  • Julian
  • Surname or Lastname

    English (common in Devon and Cornwall), Spanish (Julián), and German

    Julian

    English (common in Devon and Cornwall), Spanish (Julián), and German : from a personal name, Latin Iulianus, a derivative of Iulius (see Julius), which was borne by a number of early saints. In Middle English the name was borne in the same form by women, whence the modern girl’s name Gillian.

    Julian

  • IGNACE
  • Male

    French

    IGNACE

    French form of Latin Ignatius, possibly IGNACE means "unknowing."

    IGNACE

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  • Vote
  • n.

    Expression of judgment or will by a majority; legal decision by some expression of the minds of a number; as, the vote was unanimous; a vote of confidence.

  • Number
  • n.

    To give or apply a number or numbers to; to assign the place of in a series by order of number; to designate the place of by a number or numeral; as, to number the houses in a street, or the apartments in a building.

  • Verse
  • n.

    A line consisting of a certain number of metrical feet (see Foot, n., 9) disposed according to metrical rules.

  • Numbering
  • p. pr & vb. n.

    of Number

  • Velocity
  • n.

    Rate of motion; the relation of motion to time, measured by the number of units of space passed over by a moving body or point in a unit of time, usually the number of feet passed over in a second. See the Note under Speed.

  • Number
  • n.

    To amount; to equal in number; to contain; to consist of; as, the army numbers fifty thousand.

  • Vernier
  • n.

    A short scale made to slide along the divisions of a graduated instrument, as the limb of a sextant, or the scale of a barometer, for indicating parts of divisions. It is so graduated that a certain convenient number of its divisions are just equal to a certain number, either one less or one more, of the divisions of the instrument, so that parts of a division are determined by observing what line on the vernier coincides with a line on the instrument.

  • Volley
  • n.

    A flight of missiles, as arrows, bullets, or the like; the simultaneous discharge of a number of small arms.

  • Weetless
  • a.

    Unknowing; also, unknown; unmeaning.

  • Number
  • n.

    A numeral; a word or character denoting a number; as, to put a number on a door.

  • Knotting
  • p. pr. & vb. n.

    of Knot

  • Numbers
  • n.

    pl. of Number. The fourth book of the Pentateuch, containing the census of the Hebrews.

  • Number
  • n.

    That which is regulated by count; poetic measure, as divisions of time or number of syllables; hence, poetry, verse; -- chiefly used in the plural.

  • Number
  • n.

    The distinction of objects, as one, or more than one (in some languages, as one, or two, or more than two), expressed (usually) by a difference in the form of a word; thus, the singular number and the plural number are the names of the forms of a word indicating the objects denoted or referred to by the word as one, or as more than one.

  • Vast
  • superl.

    Very great in numbers, quantity, or amount; as, a vast army; a vast sum of money.

  • Numbered
  • imp. & p. p.

    of Number

  • Numberer
  • n.

    One who numbers.

  • Variety
  • n.

    Something varying or differing from others of the same general kind; one of a number of things that are akin; a sort; as, varieties of wood, land, rocks, etc.