The 2-bridge knots of up to 16 crossings

De Wit, D. (2007) The 2-bridge knots of up to 16 crossings. Journal of Knot Theory And Its Ramifications, 16 8: 997-1019. doi:10.1142/S021821650700566X

Author De Wit, D.
Title The 2-bridge knots of up to 16 crossings
Journal name Journal of Knot Theory And Its Ramifications   Check publisher's open access policy
ISSN 0218-2165
Publication date 2007-10
Sub-type Article (original research)
DOI 10.1142/S021821650700566X
Volume 16
Issue 8
Start page 997
End page 1019
Total pages 23
Place of publication Singapore
Publisher World Scientific Publishing
Language eng
Formatted abstract
For any given number of crossings c, there exists a formula to determine the number of 2-bridge knots of c crossings, and indeed it is a simple matter to actually construct presentations of these knots. However, the determination of whether a given (prime) knot is a 2-bridge knot remains a nontrivial exercise, and we have no procedure to determine bridge numbers more generally. Herein, we identify the 2-bridge knots within the Hoste–Thistlethwaite–Weeks tables of prime knots of up to 16 crossings by an exhaustive search of a larger set of 2-bridge knots. As the unknot is the only knot with bridge number 1, this yields a lower bound of 3 for the bridge numbers of the remaining knots.
Keyword 2-bridge knots
Links-Gould invariant
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 2 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 2 times in Scopus Article | Citations
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Created: Thu, 03 Sep 2009, 10:37:44 EST by Mr Andrew Martlew on behalf of School of Mathematics & Physics