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• Unknot (category 0 unknotting number knots and links) (section Unknotting problem)
  seen as a trivial knot In the mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the
  5 KB (560 words) - 19:08, 6 February 2024
• Knot theory (category Knot theory) (section Adding knots)
  billion knots and links (Hoste 2005). The sequence of the number of prime knots of a given crossing number, up to crossing number 16, is 0, 0, 1, 1, 2
  48 KB (6,198 words) - 19:12, 6 February 2024
• Figure-eight knot (mathematics) (category 1 unknotting number knots and links)
  Unique knot with a crossing number of four In knot theory, a figure-eight knot (also called Listing's knot) is the unique knot with a crossing number of four
  9 KB (986 words) - 18:54, 6 February 2024
• (−2,3,7) pretzel knot (category 5 unknotting number knots and links)
  Fintushel and Ronald J. Stern), is an important example of a pretzel knot which exhibits various interesting phenomena under three-dimensional and four-dimensional
  2 KB (138 words) - 20:13, 6 February 2024
• Whitehead link (category 1 unknotting number knots and links)
  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 isotopic
  6 KB (622 words) - 16:01, 6 February 2024
• Unknotting number (category Knot invariants) (section Other numerical knot invariants)
  Figure-eight knot unknotting number 1 Cinquefoil knot unknotting number 2 Three-twist knot unknotting number 1 Stevedore knot unknotting number 1 6₂ knot unknotting
  4 KB (379 words) - 22:25, 6 February 2024
• Crossing number (knot theory) (category Knot invariants)
  to crossing number. Other numerical knot invariants include the bridge number, linking number, stick number, and unknotting number. "On Knots I, II, III′"
  5 KB (565 words) - 22:45, 6 February 2024
• Unknotting problem (category Knot theory) (section Unknotting algorithms)
  result that the unknotting problem is in co-NP. Knot Floer homology of the knot detects the genus of the knot, which is 0 if and only if the knot is an unknot
  11 KB (1,220 words) - 22:16, 6 February 2024
• Prime knot (category Knot invariants)
  non-trivial knot which cannot be written as the knot sum of two non-trivial knots. Knots that are not prime are said to be composite knots or composite
  3 KB (288 words) - 21:40, 6 February 2024
• Link (knot theory) (section Tangles, string links, and braids)
  each strand required to lie at (0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (2, 1), ... – i.e., connecting the integers, and ending in the same order that they
  8 KB (1,104 words) - 22:45, 6 February 2024
• Carrick mat (category 2 unknotting number 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)
  the bridge numbers of K1 and K2. Crossing number Linking number Stick number Unknotting number Adams, Colin C. (1994), The Knot Book, American Mathematical
  3 KB (366 words) - 22:55, 6 February 2024
• Conway notation (knot theory) (category Knot theory)
  mi.sanu.ac.rs. "Conway Notation", The Knot Atlas. Conway, J.H. (1970). "An Enumeration of Knots and Links, and Some of Their Algebraic Properties". in
  3 KB (363 words) - 20:07, 6 February 2024
• Link group (category Knot invariants)
  invariants, and in fact they (and their products) are the only rational finite type concordance invariants of string links; (Habegger Masbaum). The number of linearly
  9 KB (1,196 words) - 14:58, 6 February 2024
• Alternating knot (category Knot invariants)
  diagram. Many of the knots with crossing number less than 10 are alternating. This fact and useful properties of alternating knots, such as the Tait conjectures
  6 KB (693 words) - 16:41, 6 February 2024
• 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
• List of mathematical knots and links (category Knot theory) (section Knots)
  mathematical knots and links. See also list of knots, list of geometric topology topics. 01 knot/Unknot - a simple un-knotted closed loop 31 knot/Trefoil knot
  3 KB (419 words) - 17:53, 8 February 2024
• Stick number (category Knot invariants)
  stick number for any nontrivial knot. There are few knots whose stick number can be determined exactly. Gyo Taek Jin determined the stick number of a
  5 KB (546 words) - 18:55, 8 February 2024
• Knot invariant (category Knot invariants)
  org/stable/1970594.  Rolfsen, Dale (2003). Knots and Links. Providence, RI: AMS. ISBN 0-8218-3436-3.  Adams, Colin Conrad (2004). The Knot Book: an Elementary Introduction
  10 KB (1,266 words) - 00:08, 7 February 2024
• Knot tabulation (category Knot theory)
  methods can now enumerate billions of knots in a matter of days. Knot theory Knot (mathematics) List of prime knots Unknotting problem Hoste, Jim; Thistlethwaite
  5 KB (564 words) - 15:24, 6 February 2024

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