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A concise notation based on the concept of the tangle used by Conway (1967) to enumerate prime knots up to 11 crossings. An algebraic knot containing no negative signs in its ...

The exterior of a knot K is the complement of an open solid torus knotted like K. The removed open solid torus is called a tubular neighborhood (Adams 1994, p. 258).

The second knot polynomial discovered. Unlike the first-discovered Alexander polynomial, the Jones polynomial can sometimes distinguish handedness (as can its more powerful ...

A knot K embedded in R^3=C_z×R_t, where the three-dimensional space R^3 is represented as a direct product of a complex line C with coordinate z and a real line R with ...

One of the "knots" t_(p+1), ..., t_(m-p-1) of a B-spline with control points P_0, ..., P_n and knot vector T={t_0,t_1,...,t_m}, where p=m-n-1.

A semi-oriented 2-variable knot polynomial defined by F_L(a,z)=a^(-w(L))<|L|>, (1) where L is an oriented link diagram, w(L) is the writhe of L, |L| is the unoriented diagram ...

A 2-variable oriented knot polynomial P_L(a,z) motivated by the Jones polynomial (Freyd et al. 1985). Its name is an acronym for the last names of its co-discoverers: Hoste, ...

A 1-variable unoriented knot polynomial Q(x). It satisfies Q_(unknot)=1 (1) and the skein relationship Q_(L_+)+Q_(L_-)=x(Q_(L_0)+Q_(L_infty)). (2) It also satisfies ...

A knot which is not alternating. Unlike alternating knots, flype moves are not sufficient to pass between all minimal diagrams of a given nonalternating knot (Hoste et al. ...

A generalization of spun knots due to Zeeman. This method produces four-dimensional knot types that cannot be produced by ordinary spinning.