Tight knot values deviate from linear relations

Jason Cantarella, Robert B. Kusner and John M. Sullivan ()
Additional contact information
Jason Cantarella: University of Pennsylvania
Robert B. Kusner: School of Mathematics, Institute for Advanced Study
John M. Sullivan: University of Illinois

Nature, 1998, vol. 392, issue 6673, 237-238

Abstract: Abstract Applications of knots to the study of polymers have emphasized geometric measures on curves such as ‘energy’1,2,3,4 and ‘rope length’5,6,7, which, when minimized over different configurations of a knot, give computable knot invariants related to physical quantities8. In DNA knots, electrophoretic mobility appears to be correlated with the average crossing number of rope-length-minimizing configurations9, and a roughly linear empirical relation has been observed between the crossing number and rope length10. Here we show that a linear relation cannot hold in general, and we construct infinite families of knots whose rope length grows as the 3/4 power of the crossing number11. It can be shown that no smaller power is possible12,13,14.

Date: 1998
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.nature.com/articles/32558 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nat:nature:v:392:y:1998:i:6673:d:10.1038_32558

Ordering information: This journal article can be ordered from
https://www.nature.com/

DOI: 10.1038/32558

Access Statistics for this article

Nature is currently edited by Magdalena Skipper

More articles in Nature from Nature
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().