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• Unknot (category 0 crossing number knots and links)
  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
• Borromean rings (category 6 crossing number knots and links) (section Number theory)
  in a list of all prime links with up to 13 crossings. In the tables of knots and links in Dale Rolfsen's 1976 book Knots and Links, extending earlier listings
  42 KB (4,468 words) - 20:52, 8 February 2024
• Figure-eight knot (mathematics) (category 4 crossing 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
• Crossing number (knot theory) (category Knot invariants)
  average crossing number and asymptotic crossing number. Both of these quantities bound the standard crossing number. Asymptotic crossing number is conjectured
  5 KB (565 words) - 22:45, 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
• 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
• Knot invariant (category Knot invariants)
  diagrams and taking its minimum value over all possible diagrams of a given knot. This category includes the crossing number, which is the minimum number of
  10 KB (1,266 words) - 00:08, 7 February 2024
• (−2,3,7) pretzel knot (category 12 crossing 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 5 crossing 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
• Tait conjectures (category Knot theory) (section Crossing number of alternating knots)
  again only true for alternating knots: non-alternating amphichiral knot with crossing number 15 exist. Prime knot Tangle (knot theory) Lickorish, W. B. Raymond
  6 KB (672 words) - 14:48, 6 February 2024
• L10a140 link (category 10 crossing number knots and links)
  \end{align} }[/math] David Swart, and independently Rick Mabry and Laura McCormick, discovered alternative 12-crossing visual representations of the L10a140
  6 KB (831 words) - 17:40, 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
• Jones polynomial (category Knot theory) (section Link with quantum knot invariants)
   175. ISBN 978-0-387-98254-0. https://www.springer.com/mathematics/geometry/book/978-0-387-98254-0.  Thistlethwaite, Morwen (2001). "Links with trivial Jones
  17 KB (2,344 words) - 19:41, 6 February 2024
• List of mathematical knots and links (category Knot theory) (section Knots)
  twist knot with four twists 62 knot - a prime knot with crossing number six 63 knot - a prime knot with crossing number six 71 knot, septafoil knot, (7,2)-torus
  3 KB (419 words) - 17:53, 8 February 2024
• Alexander polynomial (category Knot theory)
  particular region and crossing. If the region is not adjacent to the crossing, the entry is 0. If the region is adjacent to the crossing, the entry depends
  17 KB (2,507 words) - 19:35, 6 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
• Unknotting number (category Knot invariants) (section Other numerical knot invariants)
  determined. (The unknotting number of the 1011 prime knot is unknown.) Crossing number Bridge number Linking number Stick number Unknotting problem Adams
  4 KB (379 words) - 22:25, 6 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
• Dowker notation (category Knot theory) (section Uniqueness and counting)
  even number and the strand followed crosses over at the crossing, then change the sign on the label to be a negative. When finished, each crossing will
  3 KB (343 words) - 14:41, 6 February 2024

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