THE 2-BRIDGE KNOTS OF UP TO 16 CROSSINGS

Author:

DE WIT DAVID1

Affiliation:

1. Department of Mathematics, The University of Queensland, 4072, Brisbane, Australia

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Symmetric union presentations for 2-bridge ribbon knots;Journal of Knot Theory and Its Ramifications;2021-10

2. Equivalence of rational links and 2-bridge links revisited;Journal of Knot Theory and Its Ramifications;2015-03

3. WHERE THE LINKS–GOULD INVARIANT FIRST FAILS TO DISTINGUISH NONMUTANT PRIME KNOTS;Journal of Knot Theory and Its Ramifications;2007-10

4. Crosscap numbers of 2-bridge knots;Topology;2006-05

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