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• Tait conjectures (category Knot theory) (section Crossing number of alternating knots)
  to all knots, or just to alternating knots. It turns out that most of them are only true for alternating knots. In the Tait conjectures, a knot diagram
  6 KB (672 words) - 14:48, 6 February 2024
• Skein relation (category Knot theory)
  function F is fixed and for any triple of diagrams and their polynomials labelled as above, [math]\displaystyle{ F\Big(L_-,L_0,L_+\Big)=0 }[/math] or more
  8 KB (950 words) - 20:03, 6 February 2024
• L10a140 link (category 10 braid length knots and links)
  the second in an infinite series of Brunnian links beginning with the Borromean rings. So if the blue and yellow loops have only one twist along each side
  6 KB (831 words) - 17:40, 6 February 2024
• Stick number (category Knot invariants)
  ISBN 0-8218-3678-1 . "Stick numbers and composition of knots and links", Journal of Knot Theory and its Ramifications 6 (2): 149–161, 1997, doi:10.1142/S0218216597000121 
  5 KB (546 words) - 18:55, 8 February 2024
• Seifert surface (redirect from Knot genus) (category Knot theory) (section Genus of a knot)
  S′ of genus g + 1 and Seifert matrix [math]\displaystyle{ V' = V \oplus \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}. }[/math] The genus of a knot K is
  10 KB (1,330 words) - 23:42, 6 February 2024
• Bracket polynomial (category Knot theory)
  invariant of knots or links (as it is not invariant under type I Reidemeister moves), a suitably "normalized" version yields the famous knot invariant called
  2 KB (249 words) - 23:00, 6 February 2024
• Torus knot (section g-torus knot)
   [page needed]. ISBN 0-691-08065-8.  Rolfsen, Dale (1976). Knots and Links. Publish or Perish, Inc.. p. [page needed]. ISBN 0-914098-16-0.  Hill, Peter (December
  16 KB (1,682 words) - 22:31, 6 February 2024
• Ribbon knot (category Knots and links)
   168–176 . Reprinted by Dover Books, 2010. "Fibered knots and potential counterexamples to the property 2R and slice-ribbon conjectures", Geometry & Topology
  5 KB (564 words) - 22:35, 6 February 2024
• 2-bridge knot (category Knot theory)
  for a nontrivial knot. Other names for 2-bridge knots are rational knots, 4-plats, and Viergeflechte for 'four braids'. 2-bridge links are defined similarly
  3 KB (302 words) - 15:24, 6 February 2024
• Carrick mat (category 3 genus knots and links)
  flat, it can be used as a woggle. List of knots Budworth, Geoffrey (1999). The Ultimate Encyclopedia of Knots & Ropework. London: Hermes House. p. 227. 
  3 KB (213 words) - 00:14, 7 February 2024
• Bridge number (category Knot invariants)
  decomposed into two trivial n-tangles and hence 2-bridge knots are rational knots. If K is the connected sum of K1 and K2, then the bridge number of K is one
  3 KB (366 words) - 22:55, 6 February 2024
• Hyperbolic volume (category Knot theory) (section Knot and link invariant)
  complement is a knot invariant. In order to make it well-defined for all knots or links, the hyperbolic volume of a non-hyperbolic knot or link is often
  6 KB (626 words) - 21:17, 6 February 2024
• Finite type invariant (category Knot invariants)
  invariant of certain singular knots that vanishes on singular knots with m + 1 singularities and does not vanish on some singular knot with 'm' singularities
  5 KB (620 words) - 15:39, 6 February 2024
• HOMFLY polynomial (category Knot theory)
  + \ell^{-1}P(L_-) + mP(L_0)=0,\, }[/math] where [math]\displaystyle{ L_+, L_-, L_0 }[/math] are links formed by crossing and smoothing changes on a local
  5 KB (681 words) - 00:17, 7 February 2024
• Knot polynomial (category Knot invariants) (section Specific knot polynomials)
  List of prime knots.) Alexander polynomials and Conway polynomials can not recognize the difference of left-trefoil knot and right-trefoil knot. The left-trefoil
  6 KB (439 words) - 17:42, 6 February 2024
• Topology (category Articles with Curlie links) (section Continuous functions and homeomorphisms)
  engineering and materials science. Electrical and mechanical properties depend on the arrangement and network structures of molecules and elementary units
  35 KB (4,033 words) - 17:48, 6 February 2024
• Dowker notation (category Knot theory) (section Uniqueness and counting)
  Dowker notation is unchanged by these reflections. Knots tabulations typically consider only prime knots and disregard chirality, so this ambiguity does not
  3 KB (343 words) - 14:41, 6 February 2024
• The Knot Atlas (category Knot theory)
  "beautiful illustrations and detailed information about knots," as does KnotPlot.com. According to the site itself, it is a knot atlas (collection of maps)
  1 KB (130 words) - 15:22, 6 February 2024
• Knot tabulation (category Knot theory)
  https://zenodo.org/record/2101269  Hoste, Jim, The Enumeration and Classification of Knots and Links, http://pzacad.pitzer.edu/~jhoste/HosteWebPages/downloads/Enumeration
  5 KB (564 words) - 15:24, 6 February 2024
• Braid group (category Knot theory) (section Generators and relations)
  v=\begin{bmatrix}0 & 1 \\ -1 & 0 \end{bmatrix}, \qquad p=\begin{bmatrix}0 & 1 \\ -1 & 1 \end{bmatrix}. }[/math] Mapping a to v and b to p yields a surjective
  36 KB (4,579 words) - 15:02, 6 February 2024

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