Journal article
Rational tangle distances on knots and links
Mathematical proceedings of the Cambridge Philosophical Society, Vol.128(3), pp.497-510
05/2000
DOI: 10.1017/S0305004199004375
Abstract
In order to model biological reactions, distances between knots/links based on tangle replacement are defined. Given a tangle R, an R-move is defined as the replacement of the zero tangle in a link L with the tangle R. The R-distance between the link L and the link M is defined to be the minimum number of R-moves required to change L into M where the minimum is taken over all diagrams of the link L. A formula is given to determine when one 4-plat knot/link can be obtained from another 4-plat via one R-move when R is a rational tangle and not equal to the 1/n tangle. The formula can also be used to find all rational tangles R for which the R-distance between two given 4-plats is 1 except in the case R = 1/n tangle. These results are also generalized to the case when any rational tangle P is replaced with any rational tangle R, P not necessarily the zero tangle.
Details
- Title: Subtitle
- Rational tangle distances on knots and links
- Creators
- ISABEL K DARCY - Department of Mathematics, University of Texas, Dallas, TX 75083, U.S.A. e-mail: darcy@utdallas.eduDE WITT SUMNERS - Department of Mathematics, Florida State University, Tallahassee, FL 32306, U.S.A. e-mail: sumners@math.fsu.edu
- Resource Type
- Journal article
- Publication Details
- Mathematical proceedings of the Cambridge Philosophical Society, Vol.128(3), pp.497-510
- Publisher
- Cambridge University Press
- DOI
- 10.1017/S0305004199004375
- ISSN
- 0305-0041
- eISSN
- 1469-8064
- Number of pages
- 14
- Language
- English
- Date published
- 05/2000
- Academic Unit
- Mathematics
- Record Identifier
- 9983986091202771
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