The lower bounds of the lengths of thick knots

Journal of Knot Theory and its Ramifications

Volumn 12, Issue 1, 2003, Pages 1-16

  Diao, Yuanan ^a  

^a UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE   (United States)

Author keywords

Arc length of knots; Crossing number; Knots; Links; Thickness of knots

Indexed keywords

EID: 0037329720     PISSN: 02182165     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218216503002275     Document Type: Article

References (15)

1. C. Adams, The Knot Book, W. H. Freeman and Company, New York (1994).
2. G. Buck and J. Simon, Thickness and crossing number of knots, Topology Appl. 91(3) (1999) 245-257.
3. G. Buck, Four-thirds power law for knots and links, Nature 392 (1998) 238-239.
4. J. A. Calvo and K. C. Millett, Minimal edge piecewise linear knots, in Ideal Knots, World Scientific (1998) 107-128.
5. J. Cantarella, R. B. Kusner and J. M. Sullivan, Tight knot values deviate from linear relations, Nature 392 (1998) 237-238.
6. J. Cantarella, R. B. Kusner and J. M. Sullivan, On the minimum ropelength of knots and links, ArXiv eprint math.GT/0103224.
7. Y. Diao, The minimal knotted polygons on the cubic lattice, Journal of Knot Theory and its Ramifications 2(4) (1993) 413-425.
8. Y. Diao, The number of smallest knots on the cubic lattice, Journal of Statistical Physics 74(5) (1994) 1247-1254.
9. Y. Diao and C. Ernst, The complexity of lattice knots, Topology Appl. 90(1-3) (1998) 1-9.
10. Y. Diao, C. Ernst and E. J. Janse Van Rensburg, Knot energies by ropes, Journal of Knot Theory and its Ramifications 6(6) (1997) 799-807.
11. Y. Diao, C. Ernst and E. J. Janse Van Rensburg, Thicknesses of knots, Math. Proc. Camb. Phil. Soc. 126 (1999) 293-310.
12. M. H. Freedman and Z. He, Divergence-free fields: Energy and asymptotic crossing number, Annals of Math. 134 (1991) 189-229.
13. R. Litherland, J. Simon, O. Durumeric and E. Rawdon, Thickness of knots, Topology and its Applications 91(3) (1999) 233-244.
14. J. W. Milnor, On the total curvature of knots, Ann. Math. 52 (1950) 248-257.
15. P. Pieranski, In search of ideal knots, in Ideal Knots, World Scientific (1998) 20-41.