Link

Formally, a link is one or more disjointly embedded Circles in 3-space. More informally, a link is an assemblyof Knots with mutual entanglements. Kuperberg (1994) has shown that a nontrivial Knot or link in has four Collinear points (Eppstein). Doll and Hoste (1991) list Polynomials fororiented links of nine or fewer crossings. A listing of the first few simple links follows, arranged by CrossingNumber.

00-02-01

02-02-01

04-02-01

05-02-01

06-02-0106-02-0206-02-03

07-02-0107-02-0207-02-0307-02-0407-02-0507-02-0607-02-0707-02-08

08-02-0108-02-0208-02-0308-02-0408-02-0508-02-0608-02-0708-02-0808-02-0908-02-1008-02-1108-02-1208-02-1308-02-1408-02-1508-02-16

09-02-0109-02-0209-02-0309-02-0409-02-0509-02-0609-02-0709-02-0809-02-0909-02-1009-02-1109-02-1209-02-1309-02-1409-02-1509-02-1609-02-1709-02-1809-02-1909-02-2009-02-2109-02-2209-02-2309-02-2409-02-2509-02-2609-02-2709-02-2809-02-2909-02-3009-02-3109-02-3209-02-3309-02-3409-02-3509-02-3609-02-3709-02-3809-02-3909-02-4009-02-4109-02-4209-02-4309-02-4409-02-4509-02-4609-02-4709-02-4809-02-4909-02-5009-02-5109-02-5209-02-5309-02-5409-02-5509-02-5609-02-5709-02-5809-02-5909-02-6009-02-61

06-03-0106-03-0206-03-03

07-03-01

08-03-0108-03-0208-03-0308-03-0408-03-0508-03-0608-03-0708-03-0808-03-0908-03-10

09-03-0109-03-0209-03-0309-03-0409-03-0509-03-0609-03-0709-03-0809-03-0909-03-1009-03-1109-03-1209-03-1309-03-1409-03-1509-03-1609-03-1709-03-1809-03-1909-03-2009-03-21

08-04-0108-04-0208-04-03

09-04-01

References

Doll, H. and Hoste, J. ``A Tabulation of Oriented Links.'' Math. Comput. 57, 747-761, 1991.

Eppstein, D. ``Colinear Points on Knots.''http://www.ics.uci.edu/~eppstein/junkyard/knot-colinear.html.

Kuperberg, G. ``Quadrisecants of Knots and Links.'' J. Knot Theory Ramifications 3, 41-50, 1994.

Weisstein, E. W. ``Knots.'' Mathematica notebook Knots.m.

• Hermann's Formula
• Hermite Constants
• Hermite Differential Equation
• Hermite-Gauss Quadrature
• Hermite Interpolation
• Hermite-Lindemann Theorem
• Hermite Polynomial
• Hermite Quadrature
• Hermite's Interpolating Polynomial
• Hermite's Theorem
• Hermitian Form
• Hermitian Matrix
• Hermitian Operator
• Hermit Point
• Heronian Tetrahedron
• Heronian Triangle
• Heron's Formula
• Heron Triangle
• Herschel
• Herschfeld's Convergence Theorem
• Hessenberg Matrix
• Hesse's Theorem
• Hessian Covariant
• Hessian Determinant
• Heteroclinic Point